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2. Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras

Author

Aguiar, Marcelo, André, Carlos, Benedetti, Carolina, Bergeron, Nantel, Chen, Zhi, Diaconis, Persi, Hendrickson, Anders, Hsiao, Samuel, Isaacs, I. Martin, Jedwab, Andrea, Johnson, Kenneth, Karaali, Gizem, Lauve, Aaron, Le, Tung, Lewis, Stephen, Li, Huilan, Magaard, Kay, Marberg, Eric, Novelli, Jean-Christophe, Pang, Amy, Saliola, Franco, Tevlin, Lenny, Thibon, Jean-Yves, Thiem, Nathaniel, Venkateswaran, Vidya, Vinroot, C. Ryan, Yan, Ning, and Zabrocki, Mike

Published
2012
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4. Trace-Like Invariant for Representations of Nilpotent Liftings of Quantum Planes.

Author

Jedwab, Andrea and Krop, Leonid

Subjects
*QUANTUM groups, *NILPOTENT groups, *REPRESENTATIONS of groups (Algebra), *PLANE geometry, *MATHEMATICAL invariants, *HOPF algebras, *ENDOMORPHISMS
Abstract

We derive a formula for the trace of the antipode on endomorphism algebras of simple self-dual modules of nilpotent liftings of quantum planes. We show that the trace is equal to the quantum dimension of the module up to a nonzero scalar depending on the simple module. [ABSTRACT FROM AUTHOR]

Published
2011
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5. A Trace-Like Invariant for Representations of Hopf Algebras.

Author

Jedwab, Andrea

Subjects
*HOPF algebras, *MATHEMATICAL invariants, *ENDOMORPHISMS, *GROUP theory, *NUMERICAL analysis
Abstract

We introduce an invariant for the irreducible representations of finite dimensional Hopf algebras, defined as the trace of a map induced by the antipode on the endomorphisms of each corresponding simple module. We also compute the value of this invariant for the representations of two families of non-semisimple Hopf algebras. [ABSTRACT FROM AUTHOR]

Published
2010
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