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Verma module $V(\lambda)$ of $U_q(\mathfrak{sl}_2)$ is not simple $\implies$ $\lambda = \pm q^n$

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#abstract-algebra #lie-algebras #quantum-groups
107
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Structure of simple modules of $U_q(\mathfrak{sl}_2)$ at a root of unity.

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#abstract-algebra #representation-theory #lie-algebras #quantum-groups
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What are $q$-deformations?

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#abstract-algebra #homology-cohomology #hopf-algebras #quantum-groups #deformation-theory
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Intuition behind the relation of commutative Hopf algebra and Groups

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#abstract-algebra #lie-groups #hopf-algebras #quantum-groups
562
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Definition of the Quantum plane and the Yang Baxter Equation

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#abstract-algebra #matrix-equations #hopf-algebras #quantum-groups
329
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Quantum invariants of 2-knots

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#mathematical-physics #knot-theory #quantum-field-theory #quantum-groups #knot-invariants
163
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Integrable modules of quantum groups.

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#representation-theory #quantum-groups
140
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Bogoliubov Transform

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#group-theory #linear-transformations #quantum-mechanics #quantum-groups
452
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Reference on correspondence between commutative Hopf Algebras and Groups

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#abstract-algebra #category-theory #hopf-algebras #quantum-groups
308
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What is the relation between crystals and crystal bases?

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#representation-theory #quantum-groups
69
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Duality between comodules $SL_q(2)$ and $U_q(sl(2))$

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#abstract-algebra #representation-theory #hopf-algebras #quantum-groups
58
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Why are these endomorphisms of $U_q(\mathfrak{g})^-$

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#abstract-algebra #lie-algebras #quantum-groups
218
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Checking the antipode for the dual of the Group Hopf Algebra

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#abstract-algebra #representation-theory #hopf-algebras #quantum-groups
208
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Checking antipode on Enveloping algebra of a Lie Algebra

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#abstract-algebra #lie-algebras #hopf-algebras #quantum-groups
413
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Universal enveloping algebra vs algebra of continuous functions

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#linear-algebra #lie-groups #hopf-algebras #quantum-groups

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