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Simultaneous deformations of algebras and morphisms via derived brackets. (English) Zbl 1356.17021

Summary: We present a method to construct explicitly \(L_\infty\)-algebras governing simultaneous deformations of various kinds of algebraic structures and of their morphisms. It is an alternative to the heavy use of the operad machinery of the existing approaches. Our method relies on T. Voronov’s derived bracket construction [J. Pure Appl. Algebra 202, No. 1–3, 133–153 (2005; Zbl 1086.17012)].

MSC:

17B55 Homological methods in Lie (super)algebras
17B70 Graded Lie (super)algebras
58H15 Deformations of general structures on manifolds

Citations:

Zbl 1086.17012
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References:

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