Triviality of the automorphism group of the multiparameter quantum affine $n$-space
Ashish Gupta, Sugata Mandal

TL;DR
This paper characterizes when multiparameter quantum affine spaces have only trivial automorphisms, extending previous uniparameter results and identifying conditions based on the parameters and their generated subgroup.
Contribution
It provides necessary and sufficient conditions for the rigidity of multiparameter quantum affine spaces, generalizing automorphism results beyond the uniparameter case.
Findings
Quantum affine space automorphisms are trivial under specific parameter conditions.
Quantum tori of dimension one have trivial automorphism groups.
Expanded examples of quantum tori that are hereditary noetherian domains.
Abstract
A multiparameter quantum affine space of rank is the -algebra generated by indeterminates satisfying where are nonzero scalars in . The corresponding quantum torus is generated by the and together with their inverses subject to the same relations. So far the automorphisms of a quantum affine space have been considered mainly in the uniparameter case, that is, . We remove this restriction here. Necessary and sufficient conditions are obtained for the quantum affine space to be rigid, that is, the only automorphisms are the trivial ones arising from the action of the torus . These conditions are based on the multiparameters and also on the subgroup of generated by these multiparameters. We employ the results in J. Alev…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications
