Amitsur’s conjecture for polynomial 𝐻-identities of 𝐻-module Lie algebras

Gordienko, Alexey Sergeevich

doi:10.1090/s0002-9947-2014-06059-5

Cited by 13 publications

(29 citation statements)

References 24 publications

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“…The first author, in [18,Theorem 1] and [19,Theorem 3], proved the same for finite dimensional associative and Lie algebras graded by any group. It is well known that in the case of non-associative algebras non-integer exponents can arise.…”

Section: Introductionmentioning

confidence: 85%

Semigroup graded algebras and graded PI-exponent

2017

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Abstract. Let S be a finite semigroup and let A be a finite dimensional S-graded algebra. We investigate the exponential rate of growth of the sequence of graded codimensions c S n (A) of A, i.e lim n→∞ n c S n (A). For group gradings this is always an integer. Recently in [20] the first example of an algebra with a non-integer growth rate was found. We present a large class of algebras for which we prove that their growth rate can be equal to arbitrarily large non-integers. An explicit formula is given. Surprisingly, this class consists of an infinite family of algebras simple as an S-graded algebra. This is in strong contrast to the group graded case for which the growth rate of such algebras always equals dim(A). In light of the previous, we also handle the problem of classification of all S-graded simple algebras, which is of independent interest. We achieve this goal for an important class of semigroups that is crucial for a solution of the general problem.

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Section: Introductionmentioning

confidence: 85%

Semigroup graded algebras and graded PI-exponent

2017

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“…the graded analog of Amitsur's conjecture holds. In [7,Theorem 1] and [9,Theorem 3] the author proved the same for finite dimensional associative and Lie algebras graded by any groups. In [10] A.V.…”

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confidence: 87%

Semigroup graded algebras and codimension growth of graded polynomial identities

Gordienko

2015

Journal of Algebra

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“…Proof of Theorem 7.1. If L is semisimple, then the assertion of the theorem is a consequence of [11,Example 10]. Suppose L is not semisimple.…”

Section: Polynomial H-identitiesmentioning

confidence: 99%

Lie algebras simple with respect to a Taft algebra action

Gordienko

2019

Journal of Algebra

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We classify finite dimensional H m 2 (ζ)-simple H m 2 (ζ)-module Lie algebras L over an algebraically closed field of characteristic 0 where H m 2 (ζ) is the mth Taft algebra. As an application, we show that despite the fact that L can be non-semisimple in ordinary sense, lim n→∞ n cis the codimension sequence of polynomial H m 2 (ζ)-identities of L. In particular, the analog of Amitsur's conjecture holds for cas H m 2 (ζ)-module Lie algebras for α = 0. In Theorem 5.1 we prove that every non-semisimple H m 2 (ζ)-simple Lie algebra is

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Amitsur’s conjecture for polynomial 𝐻-identities of 𝐻-module Lie algebras

Cited by 13 publications

References 24 publications

Semigroup graded algebras and graded PI-exponent

Semigroup graded algebras and graded PI-exponent

Semigroup graded algebras and codimension growth of graded polynomial identities

Lie algebras simple with respect to a Taft algebra action

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