Equivariant Zariski Structures

Vinesh Solanki

doi:10.1112/jlms/jdv010

Equivariant Zariski Structures

Vinesh Solanki

School of Mathematics

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Abstract

A new class of noncommutative k-algebras (for k an algebraically closed field) is defined and shown to contain some important examples of quantum groups. To each such algebra, a first-order theory is assigned describing models of a suitable corresponding geometric space. Model-theoretic results for these geometric structures are established (uncountable categoricity, quantifier elimination to the level of existential formulas) and that an appropriate dimension theory exists, making them Zariski structures.

Original language	English
Pages (from-to)	786-804
Number of pages	18
Journal	Journal of the London Mathematical Society
Volume	91
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jdv010
Publication status	Published - 19 May 2015

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abstract = "A new class of noncommutative k-algebras (for k an algebraically closed field) is defined and shown to contain some important examples of quantum groups. To each such algebra, a first-order theory is assigned describing models of a suitable corresponding geometric space. Model-theoretic results for these geometric structures are established (uncountable categoricity, quantifier elimination to the level of existential formulas) and that an appropriate dimension theory exists, making them Zariski structures. ",

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AB - A new class of noncommutative k-algebras (for k an algebraically closed field) is defined and shown to contain some important examples of quantum groups. To each such algebra, a first-order theory is assigned describing models of a suitable corresponding geometric space. Model-theoretic results for these geometric structures are established (uncountable categoricity, quantifier elimination to the level of existential formulas) and that an appropriate dimension theory exists, making them Zariski structures.

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M3 - Article (Academic Journal)

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JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

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Equivariant Zariski Structures

Abstract

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