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We study cohomology of morphisms of Lie-Yamaguti algebras. As an application, we establish that this cohomology 'controls' the formal deformations. Additionally, we demonstrate its connection to the abelian extensions of morphisms of Lie-Yamaguti algebras. [ABSTRACT FROM AUTHOR]

Like quantum groups, quantum groupoids frequently appear in pairs of mutually dual objects. We develop a general Pontrjagin duality theory for quantum groupoids in the algebraic setting that extends Van Daele's duality theory for multiplier Hopf algebras and overcomes the finiteness restrictions of the approach of Kadison, Szlachányi, Böhm and Schauenburg. Our construction is based on the integration theory for multiplier Hopf algebroids and yields, as a corollary, a duality theory for weak multiplier Hopf algebras with integrals. We compute the duals in several examples and introduce morphisms of multiplier Hopf algebroids to succinctly describe their structure. Moreover, we show that such morphisms preserve the antipode. [ABSTRACT FROM AUTHOR]

In this article we provide a simple combinatorial description of morphisms between indecomposable complexes in the bounded derived category of a gentle algebra. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Niederreiter in 1991 proposed an open problem–to characterize the polynomials in Fq[x1,…,xn] which are permutation polynomials over every finite extension of Fq. The answer is well known for the case n=1. In this paper the author studies it for the case n=2 and solves the problem under a condition gcd (∂f/∂x1,∂f/∂x2,∂f/∂x2)=1 and Deg f≢0 (mod p) [Copyright &y& Elsevier]

In this paper, which is a sequel to [12] , we proceed with our study of covers and decomposition laws for geometries related to generalized quadrangles. In particular, we obtain a higher decomposition law for all Kantor-Knuth generalized quadrangles which generalizes one of the main results in [12]. In a second part of the paper, we study the set of all Kantor-Knuth ovoids (with given parameter) in a fixed finite parabolic quadrangle, and relate this set to embeddings of parabolic quadrangles into Kantor-Knuth quadrangles. This point of view gives rise to an answer of a question posed in [11]. [ABSTRACT FROM AUTHOR]