Eventually non-decreasing codimensions of *-identities

Author(s)

Shestakov, I. ; Zaicev, M.

• Document type: Journal article
• Source: ARCHIV DER MATHEMATIK; v. 116, n. 4, p. 9-pg., 2021-01-14.

Abstract

Let A be a PI-algebra. If A is an associative algebra, the sequence of codimensions c(n)(A), n = 1, 2,..., of A is asymptotically nondecreasing. For the non-associative case, there are examples of PI-algebras whose sequence of codimensions is not eventually non-decreasing. For a associative PI-algebra A with involution * : A -> A, it was recently shown that its sequence of *-codimensions c(n)*(A), n = 1, 2,..., is also asymptotically non-decreasing. In the present paper, we construct a nonassociative algebra whose sequence of *- codimensions is not eventually non-decreasing. (AU)

• FAPESP's process: 19/02510-2 - Polynomial identities and numerical invariants
• Grantee: Ivan Chestakov
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants