Decomposition of Jordan Automorphisms of Strictly Upper Triangular Matrix Algebra Over Commutative Rings

2007 ◽  
Vol 35 (4) ◽  
pp. 1133-1140 ◽  
Author(s):  
Xing Tao Wang
Keyword(s):  
Matrix Algebra ◽  
Triangular Matrix ◽  
Commutative Rings ◽  
Triangular Matrix Algebra ◽  
Upper Triangular Matrix

scholarly journals DECOMPOSITION OF JORDAN AUTOMORPHISMS OF TRIANGULAR MATRIX ALGEBRA OVER COMMUTATIVE RINGS

2010 ◽  
Vol 52 (3) ◽  
pp. 529-536 ◽  
Author(s):  
XING TAO WANG ◽  
YUAN MIN LI
Keyword(s):  
Commutative Ring ◽  
Matrix Algebra ◽  
Triangular Matrix ◽  
Commutative Rings ◽  
Graph Automorphism ◽  
Triangular Matrix Algebra ◽  
Inner Automorphism

AbstractLet Tn+1(R) be the algebra of all upper triangular n+1 by n+1 matrices over a 2-torsionfree commutative ring R with identity. In this paper, we give a complete description of the Jordan automorphisms of Tn+1(R), proving that every Jordan automorphism of Tn+1(R) can be written in a unique way as a product of a graph automorphism, an inner automorphism and a diagonal automorphism for n ≥ 1.

scholarly journals The image of multilinear polynomials evaluated on 3 × 3 upper triangular matrices

2021 ◽  
Vol 29 (2) ◽  
pp. 183-186
Author(s):  
Thiago Castilho de Mello
Keyword(s):  
Matrix Algebra ◽  
Triangular Matrix ◽  
Infinite Field ◽  
Arbitrary Degree ◽  
Triangular Matrices ◽  
Upper Triangular Matrices ◽  
Triangular Matrix Algebra ◽  
Upper Triangular Matrix ◽  
Multilinear Polynomials

Abstract We describe the images of multilinear polynomials of arbitrary degree evaluated on the 3×3 upper triangular matrix algebra over an infinite field.

scholarly journals The Minimum Number of Idempotent Generators of an Upper Triangular Matrix Algebra

1998 ◽  
Vol 205 (2) ◽  
pp. 605-616 ◽  
Author(s):  
A.V Kelarev ◽  
A.B van der Merwe ◽  
L van Wyk
Keyword(s):  
Matrix Algebra ◽  
Triangular Matrix ◽  
Triangular Matrix Algebra ◽  
Minimum Number ◽  
Upper Triangular Matrix

scholarly journals A Class of Nonlinear Nonglobal Semi-Jordan Triple Derivable Mappings on Triangular Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiuhai Fei ◽  
Haifang Zhang
Keyword(s):  
Matrix Algebra ◽  
Triangular Matrix ◽  
Nest Algebra ◽  
Triangular Algebra ◽  
Triangular Matrix Algebra ◽  
Free Block ◽  
Upper Triangular Matrix ◽  
Triangular Algebras ◽  
Torsion Free

In this paper, we proved that each nonlinear nonglobal semi-Jordan triple derivable mapping on a 2-torsion free triangular algebra is an additive derivation. As its application, we get the similar conclusion on a nest algebra or a 2-torsion free block upper triangular matrix algebra, respectively.

scholarly journals Decomposition of Automorphisms of Certain Solvable Subalgebra of Symplectic Lie Algebra over Commutative Rings

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Xing Tao Wang ◽  
Lei Zhang
Keyword(s):  
Automorphism Group ◽  
Commutative Ring ◽  
Lie Algebra ◽  
Triangular Matrix ◽  
Commutative Rings ◽  
Explicit Description ◽  
Upper Triangular Matrix

LetCl+1(R)be the2(l+1)×2(l+1)matrix symplectic Lie algebra over a commutative ringRwith 2 invertible. Thentl+1CR  =  {m-1m-20-m-1T ∣ m̅1is anl+1upper triangular matrix,m̅2T=m̅2,  over  R}is the solvable subalgebra ofCl+1(R). In this paper, we give an explicit description of the automorphism group oftl+1(C)(R).

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