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Deformed commutators on comodule algebras over coquasitriangular Hopf algebras

Zhongwei Wang, Guoyin Zhang, Liangyun Zhang (2015)

Colloquium Mathematicae

We construct quantum commutators on comodule algebras over coquasitriangular Hopf algebras, so that they are quantum group coinvariant and have the generalized antisymmetry and Leibniz properties. If the coquasitriangular Hopf algebra is additionally cotriangular, then the quantum commutators satisfy a generalized Jacobi identity, and turn the comodule algebra into a quantum Lie algebra. Moreover, we investigate the projective and injective dimensions of some Doi-Hopf modules over a quantum commutative...

Derivations of the algebra $U_{q}^{+} (B_{2})$ . (Dérivations de l'algèbre $U_{q}^{+} (B_{2})$ .)

Ben Yakoub, L., Louly, A. (2009)

Beiträge zur Algebra und Geometrie

Diagonal Temperley-Lieb invariants and harmonics.

Aval, J.-C., Bergeron, F., Bergeron, N. (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

Differential smoothness of affine Hopf algebras of Gelfand-Kirillov dimension two

Tomasz Brzeziński (2015)

Colloquium Mathematicae

Two-dimensional integrable differential calculi for classes of Ore extensions of the polynomial ring and the Laurent polynomial ring in one variable are constructed. Thus it is concluded that all affine pointed Hopf domains of Gelfand-Kirillov dimension two which are not polynomial identity rings are differentially smooth.

Dual coalgebras of Jordan bialgebras and superalgebras.

Zhelyabin, V.N. (2005)

Sibirskij Matematicheskij Zhurnal