AMITSUR'S CONJECTURE FOR POLYNOMIAL H-IDENTITIES OF H-MODULE LIE ALGEBRAS

作者：Gordienko A S^*

来源：Transactions of the American Mathematical Society, 2015, 367(1): 313-354.

• Lie algebra
• polynomial identity
• grading
• Hopf algebra
• Hopf algebra action
• H-module algebra
• codimension
• cocharacter
• symmetric group
• Young diagram
• affine algebraic group

Consider a finite dimensional H-module Lie algebra L over a field of characteristic 0 where H is a Hopf algebra. We prove the analog of Amitsur's conjecture on asymptotic behaviour for codimensions of polynomial H-identities of L under some assumptions on H. In particular, the conjecture holds when H is finite dimensional semisimple. As a consequence, we obtain the analog of Amitsur's conjecture for graded codimensions of any finite dimensional Lie algebra graded by an arbitrary group and for G-codimensions of any finite dimensional Lie algebra with a rational action of a reductive affine algebraic group G by automorphisms and anti-automorphisms.

• 出版日期2015-1