Tate Lie algebra

In mathematics, a Tate Lie algebra is a topological Lie algebra over a field whose underlying vector space is a Tate space (or Tate vector space), meaning that the topology has a base of commensurable subspaces. Tate spaces were introduced by Alexander Beilinson, B. Feigin, and Barry Mazur (1991), who named them after John Tate.

An example of a Tate Lie algebra is the Lie algebra of formal power series over a finite-dimensional Lie algebra.

References

• Arkhipov, Sergey (2002), "Semiinfinite cohomology of Tate Lie algebras", Moscow Mathematical Journal 2 (1): 35–40, ISSN 1609-3321, MR 1900583 
• Beilinson, Alexander; Feigin, B.; Mazur, Barry (1991), Notes on Conformal Field Theory, Unpublished manuscript