A Natural Extension of the Universal Enveloping Algebra Functor to Crossed Modules of Leibniz Algebras
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DOI: 10.1007/s10485-016-9472-9
Abstract: The universal enveloping algebra functor between Leibniz and associative algebras defined by Loday and Pirashvili is extended to crossed modules. We prove that the universal enveloping crossed module of algebras of a crossed module of… read more here.
Keywords: enveloping algebra; crossed module; universal enveloping; crossed modules ... See more keywords
Crossed Modules of Monoids III. Simplicial Monoids of Moore Length 1
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DOI: 10.1007/s10485-020-09603-z
Abstract: This is the last part of a series of three strongly related papers in which three equivalent structures are studied: Internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen… read more here.
Keywords: simplicial monoids; moore length; crossed modules; modules monoids ... See more keywords
A comonadic interpretation of Baues–Ellis homology of crossed modules
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DOI: 10.1007/s40062-018-0225-3
Abstract: We introduce and study a homology theory of crossed modules with coefficients in an abelian crossed module. We discuss the basic properties of these new homology groups and give some applications. We then restrict our… read more here.
Keywords: homology crossed; comonadic interpretation; baues ellis; interpretation baues ... See more keywords
Some properties of isoclinisms of Lie algebra crossed modules
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DOI: 10.1142/s1793557120500552
Abstract: Let [Formula: see text] be a Lie algebra crossed module. In this paper, we shall introduce a chain of crossed modules of [Formula: see text] and show that if [Formula: see text] and [Formula: see… read more here.
Keywords: crossed modules; see text; formula see; lie algebra ... See more keywords