Zariski closed algebras in varieties of universal algebra.
type: Item
instance of: scholarly article
title: Zariski closed algebras in varieties of universal algebra.
zbMATH Open document ID: 1315.16020
author: Antonio Giambruno
author: Louis Rowen
author: Uzi Vishne
author: A. Ya Belov
published in: Algebras and Representation Theory
publication date: 2015-01-07T00:00:00Z
review text: The authors study identical relations of algebras in the general context of universal algebra. An algebra \(A\) is representable if it is a subalgebra of a finite dimensional algebra \(B\) over a larger base field. The purpose of this paper is to develop the theory of the Zariski closure of a representable algebra (not necessarily associative) over an arbitrary integral domain. As an application, the authors prove that the codimension sequence of any representable Zariski-closed PI-algebra over an arbitrary field is exponentially bounded.
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 16R30
Mathematics Subject Classification ID: 17A01
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 17C05
zbMATH DE Number: 6384237
zbMATH Keywords: Zariski closed algebras
zbMATH Keywords: polynomial identities
zbMATH Keywords: codimension sequences
zbMATH Keywords: T-ideals
zbMATH Keywords: affine algebras
zbMATH Keywords: representable algebras
zbMATH Keywords: universal algebras
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
full work available at URL: s10468-014-9469-8
OpenAlex ID: W2144000324
cites work: Graded polynomial identities and exponential growth
cites work: The sequence of codimensions of PI-algebras
cites work: Graded polynomial identities of matrices
cites work: Q4658075
cites work: Structure of Zariski-closed algebras
cites work: PI-varieties associated to full quivers of representations of algebras.
cites work: Specht’s problem for associative affine algebras over commutative Noetherian rings
cites work: Codimension Growth of Strong Lie Nilpotent Associative Algebras
cites work: Properties of hook Schur functions with applications to P. I. algebras
cites work: Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities
cites work: Q5532570
cites work: Q3910579
cites work: Exact asymptotic behaviour of the codimensions of some P.I. algebras
cites work: Graded polynomial identities and codimensions: computing the exponential growth.
cites work: Exponential codimension growth of PI algebras: an exact estimate
cites work: Q5714236
cites work: Proper identities, Lie identities and exponential codimension growth.
cites work: Q2998334
cites work: Codimensions of polynomial identities of representations of Lie algebras
cites work: Algebras with a Scheme of Operators
cites work: Q3882586
cites work: IDENTITIES OF FINITELY GENERATED ALGEBRAS OVER AN INFINITE FIELD
cites work: Identities of associative algebras
cites work: Q3275000
cites work: Growth in varieties of Lie algebras
cites work: Growth of polynilpotent varieties of Lie algebras and rapidly growing entire functions
cites work: Q3916700
cites work: Q4314482
cites work: The representations of \(S_n\) and explicit identities for P. I. algebras
cites work: Q3910639
cites work: Q4236280
cites work: Varieties of Lie algebras with the identity \([[x_ 1,x_ 2,x_ 3],[x_ 4,x_ 5,x_ 6]]=0\) over a field of characteristic zero
cites work: Integrality of exponents of codimension growth of finite-dimensional Lie algebras
cites work: Algebras satisfying Capelli identities
DOI: 10.1007/S10468-014-9469-8
description: scientific article; zbMATH DE number 6384237