The representation dimension of quantum complete intersections
Petter Andreas Bergh, Steffen Oppermann
TL;DR
This paper investigates the representation dimension of quantum complete intersections, establishing upper bounds and demonstrating that for certain homogeneous cases, this dimension exceeds the codimension, revealing new structural insights.
Contribution
It provides the first bounds on the representation dimension of quantum complete intersections and distinguishes between homogeneous and general cases.
Findings
Representation dimension is at most twice the codimension.
Homogeneous quantum complete intersections have representation dimension greater than their codimension.
New bounds and distinctions in the structure of quantum complete intersections.
Abstract
We study the representation dimension of the class of algebras known as quantum complete intersections. For such an algebra, we show that the representation dimension is at most twice its codimension. Moreover, we show that the representation dimension of a "homogeneous" quantum complete intersection is strictly larger than its codimension.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Rings, Modules, and Algebras