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The Tensor Category of Linear Maps and Leibniz Algebras
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J. L. Loday
Published/Copyright:
February 23, 2010
Abstract
We equip the category 
of linear maps of vector spaces with a tensor product which makes it suitable for various constructions related to Leibniz algebras. In particular, a Leibniz algebra becomes a Lie object in and the universal enveloping algebra functor UL from Leibniz algebras to associative algebras factors through the category of cocommutative Hopf algebras in . This enables us to prove a Milnor–Moore type theorem for Leibniz algebras.
Received: 1996-04-29
Published Online: 2010-02-23
Published in Print: 1998-June
© 1998 Plenum Publishing Corporation
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Articles in the same Issue
- Oscillatory Properties of Solutions of Impulsive Differential Equations with Several Retarded Arguments
- Allied Integrals, Functions, and Series for the Unit Sphere
- Spectral and Boundedness Radii in Locally Convex Algebras
- The Contact Problem for an Elastic Orthotropic Plate Supported by Periodically Located Bars of Equal Resistance
- On the Solvability of Nonlinear Boundary Value Problems for Functional Differential Equations
- The Tensor Category of Linear Maps and Leibniz Algebras
- On Some Properties of Multiple Moduli of Continuity
- On Some Contact Problems for Bodies with Elastic Inclusions
