Bar Simplicial Modules and Secondary Cyclic (Co)homology

2016/05/11 by Laubacher, Jacob, Staic, Mihai D., Stancu, Alin
#16E40 (Primary) #18G30 #19D55 (Secondary) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1605.03273

Abstract

In this paper we study the simplicial structure of the complex C^\bullet((A,B,ε); M), associated to the secondary Hochschild cohomology. The main ingredient is the simplicial object B(A,B,ε), which plays a role equivalent to that of the bar resolution associated to an algebra. We also introduce the secondary cyclic (co)homology and establish some of its properties (Theorems 3.9 and 4.11).

Related

• Replacing bar-like resolutions in a simplicial setting
• Simplicial Structures Over the 3-Sphere and Generalized Higher Order\n Hochschild Homology
• Noncommutative Differential Calculus Structure on Secondary Hochschild\n (co)homology
• Properties of the Secondary Hochschild Homology
• The cyclic bar construction and fundamental groups