Homogeneous involutions on graded division algebras and their polynomial identities

被引：1

作者：

Yasumura, Felipe Yukihide ^{[1
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, Dept Math, Sao Paulo, Brazil

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2024年 / 23卷 / 09期

基金：

巴西圣保罗研究基金会;

关键词：

Homogeneous involution; polynomial identities; GRADINGS; MATRICES;

D O I：

10.1142/S0219498824501329

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by Fonseca and Mello, a homogeneous involution naturally appears when dealing with graded polynomial identities and a compatible involution.

引用

页数：11

共 13 条

[1] GRADED IDENTITIES OF MATRIX ALGEBRAS AND THE UNIVERSAL GRADED ALGEBRA [J].

Aljadeff, Eli ;

Haile, Darrell ;

Natapov, Michael .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (06) :3125-3147

[2] Distinguishing simple algebras by means of polynomial identities [J].

Bahturin, Yuri ;

Yasumura, Felipe .

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2019, 13 (01) :39-72

[3] Graded polynomial identities as identities of universal algebras [J].

Bahturin, Yuri ;

Yasumura, Felipe .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 562 :1-14

[4] Degree-inverting involution on full square and triangular matrices [J].

da Fonseca, Lais S. ;

Santulo, Ednei A., Jr. ;

Yasumura, Felipe Y. .

LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (10) :1980-1994

[5] Homogeneous involutions on upper triangular matrices [J].

de Mello, Thiago Castilho .

ARCHIV DER MATHEMATIK, 2022, 118 (04) :365-374

[6] Gradings on the algebra of upper triangular matrices and their graded identities [J].

Di Vincenzo, OM ;

Koshlukov, P ;

Valenti, A .

JOURNAL OF ALGEBRA, 2004, 275 (02) :550-566

[7]

Elduque M., 2013, GRADINGS SIMPLE LIE

[8] Graded polynomial Identities for matrices with the transpose involution over an infinite field [J].

Goncalves Fonseca, Luis Felipe ;

de Mello, Thiago Castilho .

COMMUNICATIONS IN ALGEBRA, 2018, 46 (04) :1630-1640

[9] Degree-inverting involutions on matrix algebras [J].

Goncalves Fonseca, Luis Felipe ;

de Mello, Thiago Castilho .

LINEAR & MULTILINEAR ALGEBRA, 2018, 66 (06) :1104-1120

[10] Graded polynomial identities for matrices with the transpose involution [J].

Haile, Darrell ;

Natapov, Michael .

JOURNAL OF ALGEBRA, 2016, 464 :175-197

← 1 2 →