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A generalized Courant algebroid structure is defined on the direct sum bundle DE ⊕ JE, where DE and JE are the gauge Lie algebroid and the jet bundle of a vector bundle E respectively. Such a structure is called an omni-Lie algebroid since it is reduced to the omni-Lie algebra introduced by A.Weinstein if the base manifold is a point. We prove that any Lie… (More)
We give a unified description of morphisms and comorphisms of Lie pseudoalgebras, showing that the both types of morphisms can be regarded as subalgebras of a Lie pseudoalgebra, called the ψ-sum. We also provide similar descriptions for morphisms and comorphisms of Lie algebroids and groupoids.
A graph G is said to be chromatic-choosable if ch(G) = χ(G). Ohba has conjectured that every graph G with 2χ(G) + 1 or fewer vertices is chromatic-choosable. It is clear that Ohba's conjecture is true if and only if it is true for complete multipartite graphs. In this paper we show that Ohba's conjecture is true for complete multipartite graphs K 4,3 * t,2… (More)
In this paper, we study Lie Rinehart bialgebras over a commutative algebra, the algebraic generalization of Lie algebroids. More precisely, we analyze the structure of action Lie Rinehart bialgebras over the polynomial ring K[t] induced by actions of Lie algebras on K[t].