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Given the notion of $C R$ -structures without torsion on a real $2 n + 1$ dimensional Lie algebra $L_{0}$ we study the problem of their classification when $L_{0}$ is a reductive algebra.

Crystal bases for the quantum queer superalgebra

Dimitar Grantcharov, Ji Hye Jung, Seok-Jin Kang, Masaki Kashiwara, Myungho Kim (2015)

Journal of the European Mathematical Society

In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_{q} (𝔮 (n))$ . We define the notion of crystal bases and prove the tensor product rule for $U_{q} (𝔮 (n))$ -modules in the category $𝒪_{int}^{\geq 0}$ . Our main theorem shows that every $U_{q} (𝔮 (n))$ -module in the category $𝒪_{int}^{\geq 0}$ has a unique crystal basis.

Crystal bases of Verma modules for quantum affine Lie algebras

Seok-Jin Kang, Masaki Kashiwara, Kailash C. Misra (1994)

Compositio Mathematica

Crystallographic actions on Lie groups and post-Lie algebra structures

Dietrich Burde (2021)

Communications in Mathematics

This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in $2017$ .

Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras

Peng Shan (2011)

Annales scientifiques de l'École Normale Supérieure

We define the $i$ -restriction and $i$ -induction functors on the category $𝒪$ of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.

Cuadrados especiales en la categoría de álgebras de Lie.

Daniel Tarazona (1982)

Stochastica

In this paper the concepts of mixed cartesian square and quasi-cocartesian square, already known in the category of groups, are adapted to the category of Lie algebras. These concepts can be used in the study of the obstructions of Lie algebra extensions in the same way that Wu has studied the obstructions of group extensions.

CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.

Jean-Louis Loday (1995)

Mathematica Scandinavica

Cyclic homology and the Lie algebra homology of matrices.

Daniel Quillen, J.-L. Loday (1984)

Commentarii mathematici Helvetici

Cyclotomic identities, Lie superalgebras and bicharacters. (Identité cyclotomique, superalgèbres de Lie et bicaractères.)

Duchamp, Gérard (1993)

Séminaire Lotharingien de Combinatoire [electronic only]

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