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Sets with two associative operations

Teimuraz Pirashvili (2003)

Open Mathematics

In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.

Spectral sequences for commutative Lie algebras

Friedrich Wagemann (2020)

Communications in Mathematics

We construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic 2 . In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley-Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.

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