Matrix stability and Morita invariance

2026/06/24 by Eugenia Ellis, Emanuel Rodríguez Cirone · 2 voices
Mathematics · #math.KT #math.RA

paper · pdf

Abstract

Let G be a group. We prove that matrix stability for either G-algebras or G-graded algebras guarantees Morita invariance. As a consequence, bivariant algebraic K-theory (either G-equivariant or G-graded) is Morita invariant. In particular, we show that if G is a finite group acting freely on a finite simplicial set X, then ℓ^X\rtimes G and ℓ^X/G are kk-equivalent. Here, ℓ^Y denotes the ℓ-algebra of piecewise polynomial functions on Y with coefficients in the ground ring ℓ.

Citations

• On the Accessibility and Controllability of Statistical Linearization for Stochastic Control: Algebraic Rank Conditions and their Genericity
• Morita equivalence for graded rings
• Algebraic kk-theory and the KH-isomorphism conjecture
• Equivariant algebraic kk-theory and adjointness theorems
• Isomorphism conjectures with proper coefficients
• Bivariant algebraic K-Theory

Discussions

• Eugenia Ellis, Emanuel Rodr\'iguez Cirone Matrix stability and Morita invariance https://arxiv.org/abs/2606.26380 [bsky, 0 points, 0 comments]
• Eugenia Ellis, Emanuel Rodr\'iguez Cirone: Matrix stability and Morita invariance https://arxiv.org/abs/2606.26380 https://arxiv.org/pdf/2606.26380 https://arxiv.org/html/2606.26380 [bsky, 0 points, 0 comments]

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