Noncommutative differential calculus, homotopy BV algebras and formality conjectures (Q2711786)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Noncommutative differential calculus, homotopy BV algebras and formality conjectures |
scientific article |
Statements
25 April 2001
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Hochschild cohomology
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strong homotopy algebra
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Gerstenhaber algebra
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formality theorem
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0.94683284
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0.9362617
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0.92174166
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0.9209218
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0.9156528
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0.91503656
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0.91103816
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0.9109459
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Noncommutative differential calculus, homotopy BV algebras and formality conjectures (English)
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The paper starts with a survey of algebraic structures appearing as non-commutative counterparts of objects from classical calculus. In particular, the Gerstenhaber algebras correspond to the graded Lie algebras of differential geometry. Stimulated by subjects like mirror symmetries, generalized period maps etc., the authors define a notion of strong homotopy Batalin-Vilkovisky algebra and apply it to deformation theory problems. Formality conjectures for Hochschild chains and cochains are formulated. Several results supporting these conjectures are proved.
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