How do algebras grow?

Abstract: The question of `how do algebras grow?', or, which functions can be realized as growth functions of algebras (associative/Lie/etc., or algebras having certain additional algebraic properties) is a major problem in the junction of several mathematical fields, including noncommutative algebra, combinatorics of (infinite) words, symbolic dynamics, self-similarity and more. We provide a novel paradigm for tackling this problem (in fact, family of problems), thereby resolving several open problems posed by experts regarding possible growth types of finitely generated associative algebras and Lie algebras. We also consider the set of growth functions as a space, and point out odd properties it admits (arbitrarily rapid holes, and convergence to outer points - with respect to some plausible notion of limits).

operator algebrasrings and algebras

Audience: researchers in the topic

Western Sydney University Abend Seminars

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