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.
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Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
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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)
[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] 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] 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)
[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)
[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: solvable group -- 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] 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)
[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)
[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)
[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)