Algebraic versions of \mathbbT² and of ℙ¹×ℙ¹ and Hochschild cohomology

2025/11/22 by Dotsenko, Vladimir, Solotar, Andrea
#FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2511.18073

Abstract

We examine the Hochschild cohomology for triangular algebras that capture some aspects of geometry and topology of the torus and of the quadric surface, and for deformations of these algebras. In particular, this shows that the cup product on the Hochschild cohomology of a triangular algebra does not generally follow the intuition coming from monomial algebras. Our examples also demonstrate that the Hochschild cohomology of a deformation of an algebra may not experience the dimension drop but still have a different cup product structure, and that the Hochschild cohomologies of deformations of two derived equivalent algebras may exhibit noticeably different behaviours.

Citations

• Isotropy groups of the action of orthogonal similarity on symmetric matrices
• Hochschild cohomology of twisted tensor products
• On the Lie algebra structure of the first Hochschild cohomology of\n gentle algebras and Brauer graph algebras
• On Incidence Algebras and their Representations
• Projective resolutions of associative algebras and ambiguities
• The cohomology structure of string algebras
• Hochschild cohomology of abelian categories and ringed spaces
• Hochschild cohomology and derived Picard groups
• The Continuous Hochschild Cochain Complex of a Scheme

Related

• Explicit Hochschild Cocycles for Gentle Algebras
• Secondary Hochschild Cohomology
• Operations on the Secondary Hochschild Cohomology
• Hochschild cohomology of triangular string algebras and its ring structure
• The cup product on Hochschild cohomology via twisting cochains and\n applications to Koszul rings