Displaying similar documents to “Characterizing Non-Matrix Properties of Varieties of Algebras in the Language of Forbidden Objects”

CB-degenerations and rigid degenerations of algebras

Adam Hajduk (2006)

Colloquium Mathematicae

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The main aim of this note is to prove that if k is an algebraically closed field and a k-algebra A₀ is a CB-degeneration of a finite-dimensional k-algebra A₁, then there exists a factor algebra Ā₀ of A₀ of the same dimension as A₁ such that Ā₀ is a CB-degeneration of A₁. As a consequence, Ā₀ is a rigid degeneration of A₁, provided A₀ is basic.

Varieties of modules over tubular algebras

Christof Geiss, Jan Schröer (2003)

Colloquium Mathematicae

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We classify the irreducible components of varieties of modules over tubular algebras. Our results are stated in terms of root combinatorics. They can be applied to understand the varieties of modules over the preprojective algebras of Dynkin type 𝔸₅ and 𝔻₄.

The lattice of varieties of fibered automata

Anna Mućka (2006)

Discussiones Mathematicae - General Algebra and Applications

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The class of all fibered automata is a variety of two-sorted algebras. This paper provides a full description of the lattice of varieties of fibred automata.

Asymptotic Behaviour of Colength of Varieties of Lie Algebras

Mishchenko, S., Zaicev, M. (2000)

Serdica Mathematical Journal

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This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and 00-15-96128. We study the asymptotic behaviour of numerical characteristics of polynomial identities of Lie algebras over a field of characteristic 0. In particular we investigate the colength for the cocharacters of polynilpotent varieties of Lie algebras. We prove that there exist polynilpotent Lie varieties with exponential and overexponential colength growth. We give the exact asymptotics...

Hyperidentities in many-sorted algebras

Klaus Denecke, Somsak Lekkoksung (2009)

Discussiones Mathematicae - General Algebra and Applications

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The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure...