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

[31] A NOTE ON MATRIX SUB-ALGEBRAS CONTAINING A FULL JORDAN BLOCK
LAFFEY, TJ
LINEAR ALGEBRA AND ITS APPLICATIONS, 1981, 37 (APR) : 187 - 189
[32] Jordan isomorphisms of triangular matrix algebras over a connected commutative ring
Beidar, KI
Bresar, M
Chebotar, MA
LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 312 (1-3) : 197 - 201
[33] Some inequalities involving determinants, eigenvalues, and Schur complements in Euclidean Jordan algebras
Gowda, M. Seetharama
Tao, Jiyuan
POSITIVITY, 2011, 15 (03) : 381 - 399
[34] Some inequalities involving determinants, eigenvalues, and Schur complements in Euclidean Jordan algebras
M. Seetharama Gowda
Jiyuan Tao
Positivity, 2011, 15 : 381 - 399
[35] JORDAN TRIPLE FORMS OF JORDAN ALGEBRAS
NEHER, E
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 87 (03) : 386 - 388
[36] Additivity of Jordan maps on Jordan algebras
Ji, Peisheng
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (1-2) : 179 - 188
[37] SOLID LINES IN AXIAL ALGEBRAS OF JORDAN TYPE 21 AND JORDAN ALGEBRAS
Desmet, Jari
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2025,
[38] JORDAN DIVISION ALGEBRAS AND THE ALGEBRAS A LAMBDA
PRICE, CM
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 70 (MAR) : 291 - 300
[39] Algebras of quotients of nonsingular Jordan algebras
Montaner, Fernando
Paniello, Irene
JOURNAL OF ALGEBRA, 2007, 312 (02) : 963 - 984
[40] ASSOCIATIVE ALGEBRAS WITH INVOLUTION AND JORDAN ALGEBRAS
JACOBSON, N
KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETESCHAPPEN-PROCEEDINGS SERIES A-MATHEMATICAL SCIENCES, 1966, 69 (02): : 202 - &

← 1 2 3 4 5 →