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Deformation Theory of Infinity Algebras

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Alice Fialowski (Eotvos Lorand University, Budapest), Michael Penkava (University of Wisconsin, Eau Claire)

Representation Theory · Submitted 11 Jan 2001

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We work out the deformation theory in terms of the Lie algebra of coderivations of an appropriate coalgebra structure and construct a universal infinitesimal deformation as well as a miniversal formal deformation.

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arXiv IDmath/0101097 (version 1)
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CitationAlice Fialowski (Eotvos Lorand University, Budapest), Eau Claire), Michael Penkava (University of Wisconsin. "Deformation Theory of Infinity Algebras." arXiv:math/0101097 (2001). https://pith.science/paper/DQSG6KEK
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,242 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; .

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy associative and Lie algebras. In all these cases the algebra structure is determined by an element of a certain graded Lie algebra which plays the role of a differential on this algebra. We work out the deformation theory in terms of the Lie algebra of coderivations of an appropriate coalgebra structure and construct a universal infinitesimal deformation as well as a miniversal formal deformation. By working at this level of generality, the main ideas involved in deformation theory stand out more clearly.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 This work explores the deformation theory of algebraic structures in a very general setting. contribution 0.91 0.84 0.06 asserted 0.96
s1 These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy associative and Lie algebras. background 0.90 0.11 0.04 asserted 0.99
s2 In all these cases the algebra structure is determined by an element of a certain graded Lie algebra which plays the role of a differential on this algebra. background 0.76 0.21 0.13 asserted 1.00
s3 We work out the deformation theory in terms of the Lie algebra of coderivations of an appropriate coalgebra structure and construct a universal infinitesimal deformation as well as a miniversal formal deformation. contribution 0.84 0.96 0.35 asserted 1.00
s4 By working at this level of generality, the main ideas involved in deformation theory stand out more clearly. interpretation 0.94 0.39 0.10 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

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Original abstract

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy associative and Lie algebras. In all these cases the algebra structure is determined by an element of a certain graded Lie algebra which plays the role of a differential on this algebra. We work out the deformation theory in terms of the Lie algebra of coderivations of an appropriate coalgebra structure and construct a universal infinitesimal deformation as well as a miniversal formal deformation. By working at this level of generality, the main ideas involved in deformation theory stand out more clearly.

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3 arXiv papers cite this in 3 sentences

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Cites it as background 2 papers
  • To our knowledge the mathematical literature on deformations of these algebras, specially when they admit central extensions, is not as vast and established as the finite dimensional cases, see however, [ref] .

    On Rigidity of 3d Asymptotic Symmetry Algebras · Introduction and motivations · 0.92

  • (See, for instance, [ref] and [ref] for a pedagogical introduction.) Our goal here is to identify the `infinity structure' that underlies tensor hierarchies.

    Leibniz Gauge Theories and Infinity Structures · Introduction · 0.99

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