Involutions in Algebras of Upper-Triangular Matrices

被引：1
作者：
Kulguskin, I. A. [1 ]
Tapkin, D. T. [1 ]
机构：
[1] Kazan Fed Univ, Kazan 420008, Russia
来源：
RUSSIAN MATHEMATICS | 2023年 / 67卷 / 06期
关键词：
involution; equivalence of involutions; algebra of upper-triangular matrices; AUTOMORPHISMS;
D O I：
10.3103/S1066369X2306004X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we investigate the classification of involutions of the first kind in algebra of upper-triangular matrices over commutative rings. In case of a field F of characteristics 2, we obtain necessary and sufficient conditions for finiteness of the set of involutions equivalence classes of T-n(F).
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页码：8 / 25
页数：18
相关论文
共 12 条
[1]  
[Anonymous], 1961, American Mathematical Society Colloquium Publications
[2]   Anti-automorphisms and involutions on (finitary) incidence algebras [J].
Brusamarello, Rosali ;
Fornaroli, Erica Z. ;
Santulo, Ednei A., Jr. .
LINEAR & MULTILINEAR ALGEBRA, 2012, 60 (02) :181-188
[3]   Automorphisms and involutions on incidence algebras [J].
Brusamarello, Rosali ;
Lewis, David W. .
LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (11) :1247-1267
[4]   CLASSIFICATION OF INVOLUTIONS ON INCIDENCE ALGEBRAS [J].
Brusamarello, Rosali ;
Fornaroli, Erica Z. ;
Santulo, Ednei A., Jr. .
COMMUNICATIONS IN ALGEBRA, 2011, 39 (06) :1941-1955
[5]   Involutions for upper triangular matrix algebras [J].
Di Vincenzo, Onofrio Mario ;
Koshlukov, Plamen ;
La Scala, Roberto .
ADVANCES IN APPLIED MATHEMATICS, 2006, 37 (04) :541-568
[6]   Anti-isomorphisms and involutions on the idealization of the incidence space over the finitary incidence algebra [J].
Fornaroli, Erica Z. ;
Pezzott, Roger E. M. .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2022, 637 :82-109
[7]  
Jacobson N., 1996, Finite-dimensional division algebras over fields, DOI [10.1007/978-3-642-02429-0, DOI 10.1007/978-3-642-02429-0]
[8]   A NOTE ON ALGEBRA AUTOMORPHISMS OF TRIANGULAR MATRICES OVER COMMUTATIVE RINGS [J].
KEZLAN, TP .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 135 :181-184
[9]   Automorphisms of Formal Matrix Algebras [J].
Krylov, P. A. ;
Norbosambuev, T. D. .
SIBERIAN MATHEMATICAL JOURNAL, 2018, 59 (05) :885-893
[10]  
Krylov P.A., 2021, Journal of Mathematical Sciences, V258, P222, DOI [10.1007/s10958-021-05543-8, DOI 10.1007/S10958-021-05543-8]
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