τ-tilting modules over triangular matrix artin algebras

2021 ◽  
pp. 1-23
Author(s):  
Yeyang Peng ◽  
Xin Ma ◽  
Zhaoyong Huang
Keyword(s):  
Matrix Algebra ◽  
Triangular Matrix ◽  
Finitely Generated ◽  
Tilting Modules ◽  
Triangular Matrix Algebra ◽  
Artin Algebras

Let [Formula: see text] and [Formula: see text] be artin algebras and [Formula: see text] the triangular matrix algebra with [Formula: see text] a finitely generated ([Formula: see text])-bimodule. We construct support [Formula: see text]-tilting modules and ([Formula: see text]-)tilting modules in [Formula: see text] from that in [Formula: see text] and [Formula: see text], and give the converse constructions under some condition.

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 Jordan automorphisms, Jordan derivations of generalized triangular matrix algebra

2005 ◽  
Vol 2005 (13) ◽  
pp. 2125-2132 ◽  
Author(s):  
Aiat Hadj Ahmed Driss ◽  
Ben Yakoub l'Moufadal
Keyword(s):  
Matrix Algebra ◽  
Triangular Matrix ◽  
Jordan Derivation ◽  
Matrix Algebras ◽  
Triangular Matrix Algebra

We investigate Jordan automorphisms and Jordan derivations of a class of algebras called generalized triangular matrix algebras. We prove that any Jordan automorphism on such an algebra is either an automorphism or an antiautomorphism and any Jordan derivation on such an algebra is a derivation.

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.

Sign in / Sign up

Export Citation Format

Share Document