Type: Article

(b, v)-algebras and their twisted modules

Bautista, R.; Pérez, E.; Salmerón, L.;

Abstract:

Let A be a strictly unital A?-category and Aˆ be its closure under shifts. The authors engage in an exploration of certain arithmetic characteristics associated with its higher operations and specific conflations within the precategory of cocycles Z(A) pertaining to the A?-category of twisted modules. They establish that Z(Aˆ) possesses a structure similar to a specialized Frobenius category. Subsequently, they demonstrate that the cohomology category H(Aˆ) bears similarity to the corresponding stable category. Ultimately, they conclude that this leads to the implication that H(Aˆ) constitutes a triangulated category. Note that, with a different language, this last result is known (see [M. Kontsevich, in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 120–139, Birkhäuser, Basel, 1995; MR1403918] and [B. Keller, Homology Homotopy Appl. 3 (2001), no. 1, 1–35; MR1854636; addendum, Homology Homotopy Appl. 4 (2002), no. 1, 25–28; MR1905779]).