TL;DR
This paper establishes a new correspondence between unoriented (1+1)-dimensional homotopy quantum field theories and extended crossed group algebras, expanding the algebraic framework for TQFTs.
Contribution
It introduces a bijective correspondence between unoriented HQFTs and extended crossed group algebras, generalizing previous algebraic models for TQFTs.
Findings
Establishes a bijection between unoriented HQFTs and extended crossed group algebras.
Generalizes the algebraic description of unoriented TQFTs.
Provides a new algebraic framework for studying unoriented quantum field theories.
Abstract
Turaev and Turner introduced a bijection between unoriented topological quantum field theories and extended Frobenius algebras. In this paper, we will show that there exists a bijective correspondence between unoriented (1 + 1)-dimensional homotopy quantum field theories and extended crossed group algebras.
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