Displaying similar documents to “On formal series and infinite products over Lie algebras.”

Ringel-Hall algebras of hereditary pure semisimple coalgebras

Justyna Kosakowska (2009)

Colloquium Mathematicae

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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.

The construction of 3-Lie 2-algebras

Chunyue Wang, Qingcheng Zhang (2018)

Czechoslovak Mathematical Journal

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We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.

Tilting slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały, Karolina Szmyt (2008)

Colloquium Mathematicae

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A class of finite-dimensional algebras whose Auslander-Reiten quivers have starting but not generalized standard components is investigated. For these components the slices whose slice modules are tilting are considered. Moreover, the endomorphism algebras of tilting slice modules are characterized.

Family algebras.

Kirillov, A.A. (2000)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Drinfeld-Sokolov hierarchies on truncated current Lie algebras

Paolo Casati (2011)

Banach Center Publications

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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.

On two tame algebras with super-decomposable pure-injective modules

Stanisław Kasjan, Grzegorz Pastuszak (2011)

Colloquium Mathematicae

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Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable...

On maximal subalgebras of central simple Malcev algebras.

Alberto C. Elduque Palomo (1986)

Extracta Mathematicae

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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]).