The dynamical U(n) quantum group
We study the dynamical analogue of the matrix algebra M(n), constructed from a dynamical R-matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/65279 |
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| Summary: | We study the dynamical analogue of the matrix algebra M(n), constructed from a dynamical R-matrix given by Etingof and
Varchenko. A left and a right corepresentation of this algebra,
which can be seen as analogues of the exterior algebra
representation, are defined and this defines dynamical quantum
minor determinants as the matrix elements of these
corepresentations. These elements are studied in more detail,
especially the action of the comultiplication and Laplace
expansions. Using the Laplace expansions we can prove that the
dynamical quantum determinant is almost central, and adjoining an
inverse the antipode can be defined. This results in the dynamical
GL(n) quantum group associated to the dynamical R-matrix. We
study a ∗-structure leading to the dynamical U(n) quantum
group, and we obtain results for the canonical pairing arising
from the R-matrix. |
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| ISSN: | 0161-1712 1687-0425 |