Displaying similar documents to “Family algebras.”

Ringel-Hall algebras of hereditary pure semisimple coalgebras

Justyna Kosakowska (2009)

Colloquium Mathematicae


We define and investigate Ringel-Hall algebras of coalgebras (usually infinite-dimensional). We extend Ringel's results [Banach Center Publ. 26 (1990) and Adv. Math. 84 (1990)] from finite-dimensional algebras to infinite-dimensional coalgebras.

On maximal subalgebras of central simple Malcev algebras.

Alberto C. Elduque Palomo (1986)

Extracta Mathematicae


In this paper the structure of the maximal elements of the lattice of subalgebras of central simple non-Lie Malcev algebras is considered. Such maximal subalgebras are studied in two ways: first by using theoretical results concerning Malcev algebras, and second by using the close connection between these simple non-Lie Malcev algebras and the Cayley-Dickson algebras, which have been extensively studied (see [4]).

Restricted and quasi-toral restricted Lie-Rinehart algebras

Bing Sun, Liangyun Chen (2015)

Open Mathematics


In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension...

Drinfeld-Sokolov hierarchies on truncated current Lie algebras

Paolo Casati (2011)

Banach Center Publications


In this paper we construct on truncated current Lie algebras integrable hierarchies of partial differential equations, which generalize the Drinfeld-Sokolov hierarchies defined on Kac-Moody Lie algebras.