Work

$$(b,\nu )$$-algebras and their twisted modules

Year: 2024

Type: article

Abstract: We give an intrinsic characterization of the closure under shifts $$\widehat{{\mathcal {A}}}$$ A ^ of a given strictly unital $$A_\infty $$ A ∞ -category $${{\mathcal {A}}}$$ A . We study some arithmetical properties of its higher operations and special conflations in the precategory of cocycles $${{\mathcal {Z}}}({{\mathcal {A}}})$$ Z ( A ) of its $$A_\infty $$ A ∞ -category of twisted modules. We exhibit a structure for $${{\mathcal {Z}}}(\widehat{{\mathcal {A}}})$$ Z ( A ^ ) similar to a special Frobenius category. We derive that the cohomology category $$\mathcal{H}(\widehat{{\mathcal {A}}})$$ H ( A ^ ) appears as the corresponding stable category and then we review how this implies that $${{\mathcal {H}}}(\widehat{\mathcal{A}})$$ H ( A ^ ) is a triangulated category.

Source: Boletín de la Sociedad Matemática Mexicana

DOI: 10.1007/s40590-024-00644-1

Authors: R. Bautista, E. Pérez, L. Salmerón

Institutions: Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Autonomous University of Yucatán

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

OpenAlex ID: W4401975483

FWCI:

Cites: 9

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Related to: 10