𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Exponential Growth for Codimensions of Some p.i. Algebras

✍ Scribed by Allan Berele; Amitai Regev

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
208 KB
Volume
241
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

By the Giambruno-Zaicev theorem for associative p.i. algebras, the exponential rate of growth of the codimensions of such a p.i. algebra is always a positive integer.

Here we calculate that integer for various generic p.i. algebras which are given by a single identity. These include Capelli-type identities and the various powers of the standard polynomials.

πŸ“œ SIMILAR VOLUMES

Involution Codimensions of Finite Dimens
Involution Codimensions of Finite Dimensional Algebras and Exponential Growth
✍ A Giambruno; M Zaicev πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 114 KB

Let F be a field of characteristic zero and let A be a finite dimensional algebra with involution ) over F. We study the asymptotic behavior of the sequence of n Ε½ . Ε½ . )-codimensions c A, ) of A and we show that Exp A, ) s lim c A, ) ' Ε½ . n n Βͺ Ο± n Ε½ . exists and is an integer. We give an expli

Exponential Codimension Growth of PI Alg
Exponential Codimension Growth of PI Algebras: An Exact Estimate
✍ A Giambruno; M Zaicev πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 235 KB

Let A be an associative PI-algebra over a field F of characteristic zero. By studying the exponential behavior of the sequence of codimensions [c n (A)] of A, we prove that Inv(A)=lim n Γ„ n c n (A) always exists and is an integer. We also give an explicit way for computing such integer: let B be a f

Sampling Theorem for Entire Functions of
Sampling Theorem for Entire Functions of Exponential Growth
✍ Jaeyoung Chung; Soon-Yeong Chung; Dohan Kim πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 105 KB

Applying the theory of generalized functions we obtain the Shannon sampling theorem for entire functions F z of exponential growth and give its error estimate which shows how much the error depends on the sampling size and bandwidth for given domain of the signal F z . As an application we obtain a