Determinants in Jordan matrix algebras

被引：2

作者：

Hamhalter, Jan ^{[1
]}

Kalenda, Ondrej F. K. ^{[2
]}

Peralta, Antonio M. ^{[3
]}

机构：

[1] Czech Tech Univ, Fac Elect Engn, Dept Math, Prague, Czech Republic

[2] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Sokolovska 86, Prague 18675 8, Czech Republic

[3] Univ Granada, Inst Matemat, Fac Ciencias, Dept Anal Matemat,Univ Granada IMAG, Granada, Spain

来源：

LINEAR & MULTILINEAR ALGEBRA | 2023年 / 71卷 / 06期

关键词：

JB*-algebra; Cartan factor of type 6; matrices of biquaternions; determinant; minimal projection;

D O I：

10.1080/03081087.2022.2049187

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a natural notion of determinants in matrix JB*-algebras, i.e. for hermitian matrices of biquaternions and for hermitian 3 x 3 matrices of complex octonions. We establish several properties of these determinants which are useful to understand the structure of the Cartan factor of type 6. As a tool, we provide an explicit description of minimal projections in the Cartan factor of type 6 and a variety of its automorphisms.

引用

页码：961 / 1002

页数：42

共 50 条

[11] Jordan Left Derivations of Generalized Matrix Algebras
Li Chen-Fang
Li Yan-Bo
Communications in Mathematical Research, 2014, 30 (04) : 301 - 306
[12] Matrix theory of unoriented membranes and Jordan algebras
Varga, P
JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (03)
[13] JORDAN DERIVATIONS AND ANTIDERIVATIONS OF GENERALIZED MATRIX ALGEBRAS
Li, Yanbo
van Wyk, Leon
Wei, Feng
OPERATORS AND MATRICES, 2013, 7 (02): : 399 - 415
[14] Jordan product determined points in matrix algebras
Zhu, Jun
Yang, Wenlei
MATHEMATICAL COMMUNICATIONS, 2013, 18 (02) : 309 - 321
[15] Local Jordan Derivations and Local Jordan Automorphisms of Upper Triangular Matrix Algebras
Yan Xia ZHAO 1
2.Department of Mathematics
Journal of Mathematical Research with Applications, 2010, (03) : 465 - 474
[16] Local Jordan Derivations and Local Jordan Automorphisms of Upper Triangular Matrix Algebras
Yan Xia ZHAO Rui Ping YAO Deng Yin WANG School of Mathematics and Information ScienceHenan Polytechnic UniversityHenan PRChinaDepartment of MathematicsChina University of Mining and TechnologyJiangsu PRChina
数学研究与评论, 2010, 30 (03) : 465 - 474
[17] Multialternating Jordan polynomials and codimension growth of matrix algebras
Giambruno, Antonio
Zaicev, Mikhail
LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 422 (2-3) : 372 - 379
[18] JORDAN DERIVATIONS ON BLOCK UPPER TRIANGULAR MATRIX ALGEBRAS
Ghahramani, Hoger
OPERATORS AND MATRICES, 2015, 9 (01): : 181 - 188
[19] NONCOMMUTATIVE MATRIX JORDAN ALGEBRAS, CAYLEY-DICKSON ALGEBRAS, AND SCHAFERS THEOREM
BROWN, RB
HOPKINS, NC
COMMUNICATIONS IN ALGEBRA, 1995, 23 (01) : 373 - 397
[20] DETERMINANTS IN QUANTUM MATRIX ALGEBRAS AND INTEGRABLE SYSTEMS
Gurevich, D. I.
Saponov, P. A.
THEORETICAL AND MATHEMATICAL PHYSICS, 2021, 207 (02) : 626 - 639

← 1 2 3 4 5 →