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Bicrossproduct Hopf Superalgebras and $D=4$ $κ$-deformed Poincaré Supergroup.

Kosi{ń}ski, P., J. Lukierski, Ma{ś}lanka, P., Jan T. Sobczyk

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Abstract

The general framework of bicrossproduct Hopf algebras given by Majid is extended to $Z_2$-graded bicrossproduct Hopf superalgebras. As examples of bicrossproduct Hopf superalgebras we provide the graded algebras of functions on undeformed as well as $κ$-deformed $D=4$ Poincaré supergroups.

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The general framework of bicrossproduct Hopf algebras given by Majid is extended to $Z_2$-graded bicrossproduct Hopf superalgebras. As examples of bicrossproduct Hopf superalgebras we provide the graded algebras of functions on undeformed as well as $κ$-deformed $D=4$ Poincaré supergroups.

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Available abstract

The general framework of bicrossproduct Hopf algebras given by Majid is extended to $Z_2$-graded bicrossproduct Hopf superalgebras. As examples of bicrossproduct Hopf superalgebras we provide the graded algebras of functions on undeformed as well as $κ$-deformed $D=4$ Poincaré supergroups.

Key concepts: Supergroup, Hopf algebra, Pure mathematics, Mathematics, Quantum group, Algebra over a field, Geology, Geochemistry

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