Noncommutative differential calculus structure on secondary Hochschild (co)homology

Authors

Apurba Das, Indian Institute of Technology Kanpur
Satyendra Kumar Mishra, Indian Statistical Institute Bangalore
Anita Naolekar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Communications in Algebra

Abstract

Let B be a commutative algebra and A be a B-algebra (determined by an algebra homomorphism (Formula presented.)). M. D. Staic introduced a Hochschild like cohomology (Formula presented.) called secondary Hochschild cohomology, to describe the non-trivial B-algebra deformations of A. J. Laubacher et al later obtained a natural construction of a new chain complex (Formula presented.) in the process of introducing the secondary cyclic (co)homology. In this paper, we establish a connection between the two (co)homology theories for B-algebra A. We show that the pair (Formula presented.) forms a noncommutative differential calculus, where (Formula presented.) denotes the homology of the complex (Formula presented.).

First Page

2349

Last Page

2365

DOI

10.1080/00927872.2021.2006209

Publication Date

1-1-2022

Comments

Open Access, Green

Recommended Citation

Das, Apurba; Mishra, Satyendra Kumar; and Naolekar, Anita, "Noncommutative differential calculus structure on secondary Hochschild (co)homology" (2022). Journal Articles. 3399.
https://digitalcommons.isical.ac.in/journal-articles/3399