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The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple.

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.

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Rational tori, semisimple orbits and the topology of hyperplane complements.

Recognizing cluster algebras of finite type.

Regular Elements of Finite Reflection Groups.

Relation between invertibility of Casimir operators and semisimplicity of quadratic Lie superalgebras.

Représentations indécomposables

Restriction to Levi subalgebras and generalization of the category $𝒪$

Ringel-Hall algebras of hereditary pure semisimple coalgebras

Root Systems and Elliptic Curves

Root systems and hypergeometric functions. I

Root systems and hypergeometric functions. II

Root systems and hypergeometric functions III

Root systems and hypergeometric functions IV

Root systems and Jacobi forms

Currently displaying 1 – 13 of 13