The GK dimension of relatively free algebras of PI-algebras

Centrone, Lucio

doi:10.1016/j.jpaa.2018.10.005

Cited by 7 publications

(7 citation statements)

References 33 publications

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“…In the present paper, we also get confirming, in the case of Taft’s Hopf algebra, a result obtained by one of the authors in [11].…”

Section: Introductionsupporting

confidence: 91%

“…Because the H m -exponent of UT 2 is 2, the previous result is an experimental confirmation of the following result obtained by one of the authors in [11] in the environment of graded algebras.…”

Section: Andsupporting

confidence: 86%

“…In the present paper, we also get the H m -cocharacter sequence of UT 2 and its colength, the relatively free H m -algebra of UT 2 is automata, the Gelfand-Kirillov dimension of the relatively free H m -algebra of UT 2 , confirming, in the case of Taft's Hopf algebra, a result obtained by one of the authors in [11].…”

Section: Introductionsupporting

confidence: 86%

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Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

Centrone

Estrada²

2022

Can. Math. Bull.

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Let F be a field of characteristic zero, and let $UT_2$ be the algebra of $2 \times 2$ upper triangular matrices over F. In a previous paper by Centrone and Yasumura, the authors give a description of the action of Taft’s algebras $H_m$ on $UT_2$ and its $H_m$ -identities. In this paper, we give a complete description of the space of multilinear $H_m$ -identities in the language of Young diagrams through the representation theory of the hyperoctahedral group. We finally prove that the variety of $H_m$ -module algebras generated by $UT_2$ has the Specht property, i.e., every $T^{H_m}$ -ideal containing the $H_m$ -identities of $UT_2$ is finitely based.

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“…In the present paper, we also get confirming, in the case of Taft’s Hopf algebra, a result obtained by one of the authors in [11].…”

Section: Introductionsupporting

confidence: 91%

Section: Andsupporting

confidence: 86%

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Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

Centrone

Estrada²

2022

Can. Math. Bull.

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“…Denoting by H ilb(B, t) the Hilbert series of an algebra B in the variable t, we have the next definition which should be considered as a generalization to the Hopf algebra case of the graded Hilbert series of an algebra as appeared for the first time in [18]. See also the paper [17] for an interesting relation with the graded exponent.…”

Section: Definition 21 a K-algebra A Is Called An H -Module Algebra Or An Algebra With An Haction If A Is A Left H -Module With Actionmentioning

confidence: 99%

Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras

Centrone

Zargeh

2021

Algebr Represent Theor

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“…Drensky and Papistas [11] showed that, under some natural restrictions, the Gelfand-Kirillov dimension of the group of tame automorphisms of relatively free algebras F n (V ) is equal to the Gelfand-Kirillov dimension of the algebra F n (V ). Centrone [9] proved a strict relation between the Gelfand-Kirillov dimension of the relatively free (graded) algebra of a PIalgebra and its (graded) exponent. Zhao and Zhang [26] offered an algorithm for computing the Gelfand-Kirillov dimension of certain type of differential difference modules.…”

Section: Introductionmentioning

confidence: 99%

Gelfand-Kirillov dimension of bicommutative algebras

Bai

Chen

Zhang

2021

Preprint

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We first offer a fast method for calculating the Gelfand-Kirillov dimension of a finitely presented commutative algebra by investigating certain finite set. Then we establish a Gröbner-Shirshov bases theory for bicommutative algebras, and show that every finitely generated bicommutative algebra has a finite Gröbner-Shirshov basis. As an application, we show that the Gelfand-Kirillov dimension of a finitely generated bicommutative algebra is a nonnegative integer.

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The GK dimension of relatively free algebras of PI-algebras

Cited by 7 publications

References 33 publications

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras

Gelfand-Kirillov dimension of bicommutative algebras

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