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

[21] Determinants in quantum matrix algebras and integrable systems
D. I. Gurevich
P. A. Saponov
Theoretical and Mathematical Physics, 2021, 207 : 626 - 639
[22] Schur-like forms for matrix Lie groups, Lie algebras and Jordan algebras
Ammar, G
Mehl, C
Mehrmann, V
LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 287 (1-3) : 11 - 39
[23] REDUCED JORDAN MATRIX ALGEBRAS OVER COMPLETE LOCAL RINGS
PETERSSON, HP
PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN SERIES A-MATHEMATICAL SCIENCES, 1978, 81 (01): : 97 - 109
[24] On injective Jordan semi-triple maps of matrix algebras
Lesnjak, G
Sze, NS
LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 414 (01) : 383 - 388
[25] CHARACTERIZING JORDAN AUTOMORPHISMS OF MATRIX ALGEBRAS THROUGH PRESERVING PROPERTIES
Semrl, Peter
OPERATORS AND MATRICES, 2008, 2 (01): : 125 - 136
[26] CHARACTERIZATION OF JORDAN {g, h}-DERIVATIONS OVER MATRIX ALGEBRAS
Ghosh, A.
Prakash, O.
JOURNAL OF ALGEBRAIC SYSTEMS, 2023, 11 (01):
[27] ADDITIVITY OF JORDAN TRIPLE PRODUCT HOMOMORPHISMS ON GENERALIZED MATRIX ALGEBRAS
Kim, Sang Og
Park, Choonkil
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2013, 50 (06) : 2027 - 2034
[28] Jordan embeddings and linear rank preservers of structural matrix algebras
Gogic, Ilja
Tomasevic, Mateo
LINEAR ALGEBRA AND ITS APPLICATIONS, 2025, 707 : 1 - 48
[29] POLYNOMIALS OF JORDAN ALGEBRAS AND PROPERTIES OF SPECIAL JORDAN ALGEBRAS
RAVATIN, J
IMMEDIAT.H
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1972, 23 (1-2): : 87 - 99
[30] Algebras of quotients of Jordan algebras
Montaner, Fernando
JOURNAL OF ALGEBRA, 2010, 323 (10) : 2638 - 2670

← 1 2 3 4 5 →