Vesselin Drensky

Polynomial identity rings

A Combinatorial Aspects in PI-Rings.- Vesselin Drensky.- 1 Basic Properties of PI-algebras.- 2 Quantitative Approach to PI-algebras.- 3 The Amitsur-Levitzki Theorem.- 4 Central Polynomials for Matrices.- 5 Invariant Theory of Matrices.- 6 The Nagata-Higman Theorem.- 7 The Shirshov Theorem for Finitely Generated PI-algebras.- 8 Growth of Codimensions of PI-algebras.- B Polynomial Identity Rings.- Edward Formanek.- 1 Polynomial Identities.- 2 The Amitsur-Levitzki Theorem.- 3 Central Polynomials.- 4 Kaplanskys Theorem.- 5 Theorems of Amitsur and Levitzki on Radicals.- 6 Posners Theorem.- 7 Every PI-ring Satisfies a Power of the Standard Identity.- 8 Azumaya Algebras.- 9 Artins Theorem.- 10 Chain Conditions.- 11 Hilbert and Jacobson PI-Rings.- 12 The Ring of Generic Matrices.- 13 The Generic Division Ring of Two 2 x 2 Generic Matrices.- 14 The Center of the Generic Division Ring.- 15 Is the Center of the Generic Division Ring a Rational Function Field?.

Graded polynomial identities of matrices

We consider G-graded polynomial identities of the p×p matrix algebra Mp(K) over a field K of characteristic 0 graded by an arbitrary group G. We find relations between the G-graded identities of the G-graded algebra Mp(K) and the (G×H)-graded identities of the tensor product of Mp(K) and the H-graded algebra Mq(K) with a fine H-grading. We also find a basis of the G-graded identities of Mp(K) with an elementary grading such that the identity component coincides with the diagonal of Mp(K).

Exact asymptotic behaviour of the codimensions of some P.I. algebras

AbstractLetcn(A) denote the codimensions of a P.I. algebraA, and assumecn(A) has a polynomial growth:

Defining Relations for the Algebra of Invariants of 2×2 Matrices

c_n (A)_{n_{ \to \infty }^ \simeq } qn^k

MULTIPLICITIES OF SCHUR FUNCTIONS IN INVARIANTS OF TWO 3×3 MATRICES

. Then, necessarily,q∈ℚ [D3]. If 1∈A, we show that

Polynomial identities for the Jordan algebra of a symmetric bilinear form

\frac{1}{{k!}} \leqslant q \leqslant \frac{1}{{2!}} - \frac{1}{{3!}} + - \cdot \cdot \cdot + \frac{{( - 1)^k }}{{k!}} \approx \frac{1}{e}