Showing papers by "Martin Markl published in 2013"
01 Jan 2013
TL;DR: In this paper, the authors study various operads of natural opera-tions on Hochschild cochains and relationships between them, and study the relationship between the operads and the relationships between the cochains.
Abstract: In this first paper of a series we study various operads of natural opera- tions on Hochschild cochains and relationships between them.
6 citations
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TL;DR: In this article, two algebraic versions of homotopy theory of rational disconnected topological spaces, one based on differential graded commutative associative algebras and the other based on complete differential graded Lie algesbras, were constructed.
Abstract: We construct two algebraic versions of homotopy theory of rational disconnected topological spaces, one based on differential graded commutative associative algebras and the other one on complete differential graded Lie algebras. As an application of the developed technology we obtain results on the structure of Maurer-Cartan spaces of complete differential graded Lie algebras.
6 citations
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TL;DR: In this paper, it was shown that the classical Koszul braces, as well as their non-commutative counterparts constructed recently by Borjeson, are the twistings of the trivial L-infinity algebra by a specific automorphism.
Abstract: In Part I we show that the classical Koszul braces, as well as their non-commutative counterparts constructed recently by Borjeson, are the twistings of the trivial L-infinity- (resp. A-infinity-) algebra by a specific automorphism. This gives an astonishingly simple proof of their properties. Using the twisting, we construct other surprising examples of braces. We finish Part 1 by discussing C-infinity-braces related to Lie algebras.
In Part 2 we prove that in fact all natural braces are the twistings by unique automorphisms. We also show that there is precisely one hierarchy of braces that leads to a sensible notion of higher-order derivations. Thus, the notion of higher-order derivations is independent of human choices. The results of the second part follow from the acyclicity of a certain space of natural operations.
3 citations
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TL;DR: In this paper, the authors give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces.
Abstract: We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras and their diagrams.
2 citations