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6 papers
Resolution of the GL(3) - O(3) state labelling problem via O(3)-invariant Bethe subalgebra of the twisted Yangian
P. D. Jarvis, R. B. Zhang
The labelling of states of irreducible representations of GL(3) in an O(3) basis is well known to require the addition of a single O(3)-invariant operator, to the standard diagonal…
Integration on Lie supergroups. A Hopf superalgebra approach
M. Scheunert, R. B. Zhang
For a large class of finite-dimensional Lie superalgebras (including the classical simple ones) a Lie supergroup associated to the algebra is defined by fixing the Hopf superalgebr…
Invariant integration on classical and quantum Lie supergroups
M. Scheunert, R. B. Zhang
Invariant integrals on Hopf superalgebras, in particular, the classical and quantum Lie supergroups, are studied. The uniqueness (up to scalar multiples) of a left integral is prov…
The second cohomology of sl(m|1) with coefficients in its enveloping algebra is trivial
M. Scheunert, R. B. Zhang
Using techniques developed in a recent article by the authors, it is proved that the 2-cohomology of the Lie superalgebra sl(m|1); m > 1, with coefficients in its enveloping algebr…
Comments on the Noncommutative Geometry of Quantum Homogeneous Vector Bundles
R. B. Zhang
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential…
Geometry of Quantum Homogeneous Supervector Bundles and Representation Theory of Quantum General Linear Supergroup
R. B. Zhang
The quantum general linear supergroup GLq(m|n) is defined and its structure is studied systematically. Quantum homogeneous supervector bundles are introduced following Connes' theo…