Strongly homotopy lie algebras

Lada, Tom; Markl, Martin

doi:10.1080/00927879508825335

Cited by 388 publications

(499 citation statements)

References 11 publications

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“…We only emphasize that an L ∞ morphism of DGLAs has a linear part that is a morphism of complexes and therefore it induces a morphism in cohomology. For the detailed descriptions of such structures we refer to [LS93,LM95,Ma02,Fu03,Kon03,Get04,Ma04,FiMa07,Ia08]. The homotopy fibre of a morphism of DGLA χ : L → M is the DGLA…”

Section: Review Of Logarithmic Differentialsmentioning

confidence: 99%

Deformations and Obstructions of Pairs (X,D)

Iacono

2014

Int Math Res Notices

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Abstract. We study infinitesimal deformations of pairs (X, D) with X smooth projective variety and D a smooth or a normal crossing divisor, defined over an algebraically closed field of characteristic 0. Using the differential graded Lie algebras theory and the Cartan homotopy construction, we are able to prove in a completely algebraic way the unobstructedness of the deformations of the pair (X, D) in many cases, e.g., whenever (X, D) is a log Calabi-Yau pair, in the case of a smooth divisor D in a Calabi Yau variety X and when D is a smooth divisor in | − mKX|, for some positive integer m.

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Section: Review Of Logarithmic Differentialsmentioning

confidence: 99%

Deformations and Obstructions of Pairs (X,D)

Iacono

2014

Int Math Res Notices

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“…The proof for Theorem 4.3 strictly follows the correspondence of such structures with degree +1 differentials on the free graded algebra S( V * ). It was proved in [13] that each strongly homotopy Lie algebra implies the existence of a differential, while the converse can be found in [12]. We refer to [18, Section 6.1] for additional details on this relation.…”

Section: Remark 311mentioning

confidence: 99%

Introduction to graded geometry

Fairon

2017

European Journal of Mathematics

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This paper aims at setting out the basics of Z-graded manifolds theory. We introduce Z-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric algebra to define functions is made clear. Moreover, we define vector fields and exhibit their graded local basis. The paper also reviews some correspondences between differential Z-graded manifolds and algebraic structures.

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“…where f n 's are, for n ≥ 1, as in (7). If the vector space V equals the ground field k, S(A * ) ⊗ k is isomorphic to S(A * ) and we obtain the standard identification of the polynomial ring S(A * ) with the algebra of regular functions on the affine space A.…”

Section: Morphismsmentioning

confidence: 99%

“…that satisfy a set of axioms saying that λ 1 is a differential, λ 2 obeys the Jacobi identity up to the homotopy λ 3 , etc., see for instance [7] or [8].…”

Section: ∞ -Algebras As Homological Vector Fieldsmentioning

confidence: 99%

Higher Braces Via Formal (Non)Commutative Geometry

Markl

2015

Trends in Mathematics

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Abstract. We translate the main result of [11] to the language of formal geometry. In this new setting we prove directly that the Koszul resp. Börjeson braces are pullbacks of linear vector fields over the formal automorphism ϕ(a) = exp(a) − 1 in the Koszul, resp. ϕ(a) = a(1 − a) −1 in the Börjeson case. We then argue that both braces are versions of the same object, once materialized in the world of formal commutative geometry, once in the non-commutative one.Mathematics Subject Classification (2010). 13D99, 14A22, 55S20.

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Strongly homotopy lie algebras

Cited by 388 publications

References 11 publications

Deformations and Obstructions of Pairs (X,D)

Deformations and Obstructions of Pairs (X,D)

Introduction to graded geometry

Higher Braces Via Formal (Non)Commutative Geometry

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