Abrams, Lowell Two-dimensional topological quantum field theories and Frobenius algebras. (English) Zbl 0897.57015 J. Knot Theory Ramifications 5, No. 5, 569-587 (1996). The relationship between two-dimensional (2-D) topological quantum field theories and Frobenius algebras \(A\) (characterized as algebras having a comultiplication which is a map of \(A\)-modules) is formulated as an equivalence of categories. A classification of the indecomposable 2-D topological quantum field theories as a result of classifying of the indecomposable Frobenius algebras (either ‘annihilator algebras’ whose socle is a principal ideal or field extensions). Eight examples are considered in the conclusion. Reviewer: A.V.Aminova (Kazan’) Cited in 2 ReviewsCited in 73 Documents MSC: 57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010) 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 57R90 Other types of cobordism Keywords:topological quantum field theory; 2-D; Frobenius algebra cobordism; category theory PDFBibTeX XMLCite \textit{L. Abrams}, J. Knot Theory Ramifications 5, No. 5, 569--587 (1996; Zbl 0897.57015) Full Text: DOI