On the stability of regular algebras
Kai Behrend, Junho Hwang
TL;DR
This paper characterizes stable quadratic regular algebras of global dimension 3, describing their moduli stack and providing the first non-trivial non-commutative examples of Behrend-Noohi stability.
Contribution
It offers a classification of stable quadratic regular algebras of dimension 3 and describes their moduli stack, introducing new non-commutative examples of stability.
Findings
Characterization of stable quadratic regular algebras of dimension 3
Description of the moduli stack of these algebras
First non-trivial non-commutative examples of Behrend-Noohi stability
Abstract
We characterize which quadratic regular algebras of global dimension 3 are stable in the sense of Behrend-Noohi. (This notion of stability is a non-commutative analogue of Hilbert stability.) We describe the quasi-projective stack of stable quadratic regular algebras of dimension 3. This provides the first non-trivial, non-commutative examples of stability a la Behrend-Noohi.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology