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Maurer-Cartan characterizations and cohomologies of compatible Lie algebras
In this paper, we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie algebras. Explicitly, we first introduce the...
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The Maurer–Cartan Form of Operator Pencils
Given a Lie group G, its Maurer–Cartan form \(\omega (g)=g^{-1}dg,\ g\in G,\)...
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Maurer–Cartan Equation and Deligne Groupoids
In this chapter we introduce the natural transformation \({{\text {Def}}}\)...
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Maurer–Cartan Moduli and Theorems of Riemann–Hilbert Type
We study Maurer–Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are...
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Maurer–Cartan Elements and the Deligne Groupoid
Whenever the dgl is complete, the set of these elements is endowed with a particular equivalence relation given by the gauge action, a particular...
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Equivariant one-parameter deformations of associative algebra morphisms
We introduce equivariant formal deformation theory of associative algebra morphisms. We also present an equivariant deformation cohomology of...
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3-pre-Leibniz Algebras, Deformations and Cohomologies of Relative Rota-Baxter Operators on 3-Leibniz Algebras
In this paper, first we introduce the notions of 3-pre-Leibniz algebras and relative Rota-Baxter operators on 3-Leibniz algebras. We show that a...
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Weak stationarity of a matrix valued differential form at superdensity points of its vanishing set
A property of weak stationarity of a matrix valued differential form at superdensity points of its vanishing set is proved. This result is then...
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Cohomology and Deformations of Compatible Lie Triple Systems
In this paper, we first introduce the notions of a compatible Lie triple system and its representation. We construct a bidifferential graded Lie...
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Hermitian Metrics on the Resolvent Set
For elements \(A_1, \ldots , A_n\) in a unital Banach algebra...
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Cohomology and deformations of twisted Rota–Baxter operators and NS-algebras
The aim of this paper is twofold. In the first part, we consider twisted Rota–Baxter operators on associative algebras that were introduced by Uchino...
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Formal Kuranishi Families and Period Maps
After the results regarding coalgebras and \(L_{\infty }\)...
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\(L_{\infty }\) -Algebras
The aim of this chapter is to present \(L_{\infty }\)...
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Smooth Rough Paths, Their Geometry and Algebraic Renormalization
We introduce the class of “smooth rough paths” and study their main properties. Working in a smooth setting allows us to discard sewing arguments and...
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Enriched Koszul duality
We show that the category of non-counital conilpotent dg-coalgebras and the category of non-unital dg-algebras carry model structures compatible with...
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Weight Decompositions on Algebraic Models for Map** Spaces and Homotopy Automorphisms
We obtain restrictions on the rational homotopy types of map** spaces and of classifying spaces of homotopy automorphisms by means of the theory of...
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Deformations of Compact Complex Manifolds with Ample Canonical Bundles
In this paper, the author discusses the deformations of compact complex manifolds with ample canonical bundles. It is known that a complex manifold...
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Regular Representation of the Group GL(N, ℝ): Factorization, Casimir Operators and Toda Chain
The note is devoted to the factorization formula for the matrix with the generators of the group GL( N , ℝ) in the regular representation. The...