Wikipedia:WikiProject Mathematics/PlanetMath Exchange/17-XX Nonassociative rings and algebras
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This page provides a list of all articles available at PlanetMath in the following topic:
- 17-XX Nonassociative rings and algebras.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status | means PM article |
N | not needed |
A | adequately covered |
C | copied |
M | merged |
NC | needs copying |
NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
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See the main page for examples and usage criteria.
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[edit] 17-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
[edit] 17-08 Computational methods
[edit] 17A01 General theory
- PM: associator, id=6348 -- WP: associator -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: commutator bracket, id=2811 -- WP: commutator -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: centralizers in algebra, id=9740new! -- WP guess: centralizers in algebra -- Status:
- PM: homotopes and isotopes of algebras, id=8614new! -- WP guess: homotopes and isotopes of algebras -- Status:
- PM: non-associative algebra, id=6845new! -- WP guess: non-associative algebra -- Status:
- PM: trace forms on algebras, id=8627new! -- WP guess: trace forms on algebras -- Status:
[edit] 17A05 Power-associative rings
- PM: power-associative algebra, id=6350 -- WP: power-associative algebra -- Status: A
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- Jtwdog 20:37, 26 September 2005 (UTC)
[edit] 17A20 Flexible algebras
- PM: flexible algebra, id=6351 -- WP guess: flexible algebra -- Status: N
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- Jtwdog 20:41, 26 September 2005 (UTC)
[edit] 17A36 Automorphisms, derivations, other operators
[edit] 17A45 Quadratic algebras (but not quadratic Jordan algebras)
- PM: quadratic algebra, id=6950new! -- WP guess: quadratic algebra -- Status:
[edit] 17A75 Composition algebras
- PM: composition algebra, id=6949new! -- WP guess: composition algebra -- Status:
- PM: composition algebra over algebaically closed fields, id=9654new! -- WP guess: composition algebra over algebaically closed fields -- Status:
- PM: composition algebras over \mathbb{Q}, id=9656new! -- WP guess: composition algebras over \mathbbQ -- Status:
- PM: composition algebras over \mathbb{R}, id=9652new! -- WP guess: composition algebras over \mathbbR -- Status:
- PM: composition algebras over finite fields, id=9655new! -- WP guess: composition algebras over finite fields -- Status:
- PM: Hurwitz's theorem on composition algebras, id=9653new! -- WP guess: Hurwitz's theorem on composition algebras -- Status:
- PM: Jacobson's theorem on composition algebras, id=9651new! -- WP guess: Jacobson's theorem on composition algebras -- Status:
[edit] 17A99 Miscellaneous
- PM: Cayley-Dickson construction, id=6586 -- WP: Cayley-Dickson construction -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
[edit] 17Axx General nonassociative rings
[edit] 17B01 Identities, free Lie (super)algebras
- PM: Lie superalgebra, id=7509new! -- WP guess: Lie superalgebra -- Status:
- PM: quadratic Lie algebra, id=7379new! -- WP guess: quadratic Lie algebra -- Status:
[edit] 17B05 Structure theory
- PM: Killing form, id=3743 -- WP: Killing form -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Levi's theorem, id=4592 -- WP guess: Levi's theorem -- Status: NC
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: nilradical, id=4594 -- WP: nilradical -- Status: NC
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- Jtwdog 20:13, 26 September 2005 (UTC)
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- For radical and nilradical, there are already wikipedia for the related notions for associative algebras. I personally, think these should be merged into an article on solvable and nilpotent Lie algebras, which doesn't seem to exist. Jtwdog 20:13, 26 September 2005 (UTC)
- PM: index of a Lie algebra, id=7380new! -- WP guess: index of a Lie algebra -- Status:
- PM: regular element of a Lie algebra, id=7382new! -- WP guess: regular element of a Lie algebra -- Status:
[edit] 17B10 Representations, algebraic theory (weights)
- PM: adjoint representation, id=2965 -- WP: adjoint representation -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Ado's theorem, id=3861 -- WP guess: representations of Lie algebras -- Status: NM
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- Jtwdog 21:00, 26 September 2005 (UTC)
- PM: examples of non-matrix Lie groups, id=3864 -- WP: representations of Lie groups -- Status: NM
- Alternatively, there could be a page incorporationing Ado's theorem, these examples, and similar things.
- Jtwdog 21:00, 26 September 2005 (UTC)
- PM: isotropy representation, id=2992 -- WP guess: isotropy representation -- Status: NC
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- Jtwdog 21:00, 26 September 2005 (UTC)
- PM: Lie algebra representation, id=2966 -- WP guess: representations of Lie algebras -- Status: NM
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- Jtwdog 21:00, 26 September 2005 (UTC)
[edit] 17B15 Representations, analytic theory
- PM: invariant form (Lie algebras), id=3742 -- WP: representations of Lie algebras -- Status: NM
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- Jtwdog 21:01, 26 September 2005 (UTC)
[edit] 17B20 Simple, semisimple, reductive (super)algebras (roots)
- PM: Borel subalgebra, id=3666 -- WP: Borel subalgebra -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Borel subgroup, id=4035 -- WP guess: Borel subgroup -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Cartan matrix, id=3799 -- WP: Cartan matrix -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Cartan subalgebra, id=3849 -- WP: Cartan subalgebra -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Cartan's criterion, id=3744 -- WP guess: Cartan's criterion -- Status: N
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Casimir operator, id=4624 -- WP: Casimir operator -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: classification of finite-dimensional representations of semi-simple Lie algebras, id=3653 -- WP: Representations of Lie groups -- Status: NM
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- Jtwdog 20:50, 26 September 2005 (UTC)
- PM: cohomology of semi-simple Lie algebras, id=4591 -- WP: Lie algebra cohomology -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Dynkin diagram, id=4037 -- WP: Dynkin diagram -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: nilpotent cone, id=4748 -- WP: nilpotent cone -- Status: C
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- Jtwdog 18:23, 28 October 2005 (UTC)
- PM: parabolic subgroup, id=4036 -- WP: parabolic subgroup -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: pictures of Dynkin diagrams, id=4060 -- WP: Dynkin diagram -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: positive root, id=3656 -- WP: positive root -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: rank (Lie algebra), id=2348 -- WP: Cartan subalgebra -- Status: NM
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- Jtwdog 20:50, 26 September 2005 (UTC)
- PM: root lattice, id=3659 -- WP: weight (representation theory) -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: root system, id=3645 -- WP: root system -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: simple and semi-simple Lie algebras, id=3644 -- WP: simple Lie group -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: simple root, id=3657 -- WP: simple root -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Verma module, id=3665 -- WP guess: Verma module -- Status: C
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- Jtwdog 18:24, 28 October 2005 (UTC)
- PM: weight (Lie algebras), id=3654 -- WP: weight (representation theory) -- Status: NM
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- Jtwdog 20:50, 26 September 2005 (UTC)
- PM: weight lattice, id=3660 -- WP: weight (representation theory) -- Status: NM
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- Jtwdog 20:50, 26 September 2005 (UTC)
- PM: Weyl chamber, id=3661 -- WP: Weyl chamber -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Weyl group, id=3658 -- WP: Weyl group -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Weyl's theorem, id=3877 -- WP guess: Weyl's theorem -- Status: N
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: classification of indecomposable root systems, id=7337new! -- WP guess: classification of indecomposable root systems -- Status:
- PM: root system underlying a semi-simple Lie algebra, id=7338new! -- WP guess: root system underlying a semi-simple Lie algebra -- Status:
[edit] 17B30 Solvable, nilpotent (super)algebras
- PM: Lie's theorem, id=3860 -- WP guess: Lie's theorem -- Status: C
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- Jtwdog 18:24, 28 October 2005 (UTC)
- PM: solvable Lie algebra, id=2964 -- WP: Lie algebra -- Status: NM
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- As I said before, I think it's worth just having a separate page on solvable and nilpotent Lie algebras which covers all this business. Jtwdog 20:13, 26 September 2005 (UTC)
[edit] 17B35 Universal enveloping (super)algebras
- PM: Poincaré-Birkhoff-Witt theorem, id=3467 -- WP: Poincaré-Birkhoff-Witt theorem -- Status: A
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- Something should be done about correctly copying over é (or maybe it's not worth it). Jtwdog 20:13, 26 September 2005 (UTC)
- PM: universal enveloping algebra, id=3466 -- WP: universal enveloping algebra -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
[edit] 17B56 Cohomology of Lie (super)algebras
- PM: Lie algebra cohomology, id=4589 -- WP: Lie algebra cohomology -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
[edit] 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[edit] 17B67 Kac-Moody (super)algebras (structure and representation theory)
- PM: generalized Cartan matrix, id=4625 -- WP: generalized Cartan matrix -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Kac-Moody algebra, id=4124 -- WP: Kac-Moody algebra -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: extended Cartan matrix, id=7363new! -- WP guess: extended Cartan matrix -- Status:
[edit] 17B70 Graded Lie (super)algebras
[edit] 17B99 Miscellaneous
- PM: Jacobi identity interpretations, id=3468 -- WP: Jacobi identity -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Lie algebra, id=1113 -- WP: Lie algebra -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: local Nagano theorem, id=6464 -- WP guess: local Nagano theorem -- Status: N
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- Jtwdog 20:13, 26 September 2005 (UTC)
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Heisenberg algebra, id=7259new! -- WP guess: Heisenberg algebra -- Status:
- PM: Lie algebras from other algebras, id=8825new! -- WP guess: Lie algebras from other algebras -- Status:
- PM: modular theory, id=8601new! -- WP guess: modular theory -- Status:
- PM: restricted Lie algebra, id=8602new! -- WP guess: restricted Lie algebra -- Status:
[edit] 17Bxx Lie algebras and Lie superalgebras
[edit] 17C05 Identities and free Jordan structures
- PM: Jordan algebra, id=6547 -- WP: Jordan algebra -- Status: A
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- Jtwdog 20:13, 26 September 2005 (UTC)
- PM: Jordan triple product, id=8615new! -- WP guess: Jordan triple product -- Status:
- PM: quadratic Jordan algebra, id=8626new! -- WP guess: quadratic Jordan algebra -- Status:
[edit] 17Cxx Jordan algebras (algebras, triples and pairs)
[edit] 17D05 Alternative rings
- PM: alternative algebra, id=6349 -- WP: alternative algebra -- Status: NM
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- Jtwdog 20:13, 26 September 2005 (UTC)