𝔖 Bobbio Scriptorium
✦   LIBER   ✦

New Automorphisms of Generic Matrix Algebras and Polynomial Algebras

✍ Scribed by Vesselin Drensky; C.K. Gupta

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
148 KB
Volume
194
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let T be the generic trace algebra generated by the algebra R of two generic 2 = 2 matrices and by all traces of the matrices from R over a field K. We construct new automorphisms of T and R. They induce automorphisms of the polynomial algebra in five variables which fix two of the variables. Our automorw x phisms of R are wild. We do not know if the new automorphisms of K x , . . . , x 1 5 are tame. When char K / 2 we give the explicit form of all the constructed automorphisms.

πŸ“œ SIMILAR VOLUMES

New Stably Tame Automorphisms of Polynom
New Stably Tame Automorphisms of Polynomial Algebras
✍ Vesselin Drensky; Arno van den Essen; Dimitre Stefanov πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 93 KB

Let K X Y = K x 1 x n y 1 y m be the polynomial algebra in m + n variables over a field K of characteristic 0. Let Ξ΄ be a locally nilpotent derivation of K X Y such that Ξ΄ y i = 0, i = 1 m, and let Ξ΄ act as a K Y -affine transformation over the free K Y -module freely generated by x 1 x n . We pro

Test Polynomials for Automorphisms of Po
Test Polynomials for Automorphisms of Polynomial and Free Associative Algebras
✍ Vesselin Drensky; Jie-Tai Yu πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 229 KB

In this paper we consider test polynomials in the polynomial algebra and the free associative algebra. A test polynomial is defined by the following property: every endomorphism which fixes the polynomial is an automorphism. We construct families of test polynomials for the polynomial algebra and th

Matrix Algebras with Involution and Cent
Matrix Algebras with Involution and Central Polynomials
✍ Tsetska Rashkova πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 118 KB

In this paper we study central polynomials for the matrix algebra M 2n K \* with symplectic involution \* . Their form is inspired by an apporach of Formanek and Bergman for investigating matrix identities by means of commutative algebra. We continue the investigations started earlier (1999,

Algebraic Aspects of Matrix Orthogonalit
Algebraic Aspects of Matrix Orthogonality for Vector Polynomials
✍ Vladimir N. Sorokin; Jeannette Van Iseghem πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 355 KB

An algebraic theory of orthogonality for vector polynomials with respect to a matrix of linear forms is presented including recurrence relations, extension of the Shohat Favard theorem, of the Christoffel Darboux formula, and its converse. The connection with orthogonal matrix polynomials is describ