POLYNOMIAL IDENTITIES WITH INVOLUTION, SUPERINVOLUTIONS AND THE GRASSMANN ENVELOPE

被引：30

作者：

Aljadeff, Eli ^{[1
]}

Giambruno, Antonio ^{[2
]}

Karasik, Yakov ^{[1
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[2] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 34, I-90123 Palermo, Italy

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 05期

基金：

以色列科学基金会;

关键词：

Polynomial identity; involution; superinvolution; Grassmann algebra; PI ALGEBRAS;

D O I：

10.1090/proc/13546

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A be an algebra with involution * over a field of characteristic zero. We prove that in case A satisfies a non-trivial *-identity, then A has the same *-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i. e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.

引用

页码：1843 / 1857

页数：15

共 12 条

[1] Kemer's theorem for affine PI algebras over a field of characteristic zero [J].

Aljadeff, Eli ;

Kanel-Belov, Alexei ;

Karasik, Yaakov .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2016, 220 (08) :2771-2808

[2] Representability and Specht problem for G-graded algebras [J].

Aljadeff, Eli ;

Kanel-Belov, Alexei .

ADVANCES IN MATHEMATICS, 2010, 225 (05) :2391-2428

[3] IDENTITIES IN RINGS WITH INVOLUTIONS [J].

AMITSUR, SA .

ISRAEL JOURNAL OF MATHEMATICS, 1969, 7 (01) :63-&

[4] COCHARACTERS, CODIMENSIONS AND HILBERT SERIES OF THE POLYNOMIAL-IDENTITIES FOR 2X2 MATRICES WITH INVOLUTION [J].

DRENSKY, V ;

GIAMBRUNO, A .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1994, 46 (04) :718-733

[5] WREATH-PRODUCTS AND PI ALGEBRAS [J].

GIAMBRUNO, A ;

REGEV, A .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1985, 35 (02) :133-149

[6] Varieties of Algebras with Superinvolution of Almost Polynomial Growth [J].

Giambruno, Antonio ;

Ioppolo, Antonio ;

La Mattina, Daniela .

ALGEBRAS AND REPRESENTATION THEORY, 2016, 19 (03) :599-611

[7]

Giambruno Antonio, 2005, MATH SURVEYS MONOGRA, V122

[8] Amitsur's conjecture for associative algebras with a generalized Hopf action [J].

Gordienko, A. S. .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2013, 217 (08) :1395-1411

[9] Kemer's theory for H-module algebras with application to the PI exponent [J].

Karasik, Yaakov .

JOURNAL OF ALGEBRA, 2016, 457 :194-227

[10]

Kemer Aleksandr Robertovich, 1991, TRANSLATIONS MATH MO, V87

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