#20029: Implement quantum matrix coordinate algebras
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.1
Component: algebra | Resolution:
Keywords: quantum, | Merged in:
coordinate ring | Reviewers: Daniel Bump, Valentin
Authors: Travis Scrimshaw | Buciumas
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/algebras/quantum_matrix_coordinate_ring-20029|
691b99d2e6e351bc42edb60561c9c9389d45dcd8
Dependencies: | Stopgaps:
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Comment (by buciumas):
I don't think there is a formula for the inverse of the q-determinant in
GL_q(n). I think GL_q(n) is defined as the bialgebra generated by the
regular generators plus a generator c that is central mod the relation c *
qdet = 1. So you can write the antipode in GL_q(n) as a sum of products of
the x_{ij}'s and multiply everything by the inverse of the qdet. In the
case of SL_q(n) qdet is set to 1. In the case of the quantum coordinate
ring which you implemented you can't write a formula for the antipode
because qdet is not invertible or equal to 1.
Formulas for the antipode and qdet (which I think you already know) for
SL_q(n) can be found (among many places) here :
http://arxiv.org/abs/1602.04262 (page 16 last formula and page 17 first
formula).
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Ticket URL: <http://trac.sagemath.org/ticket/20029#comment:12>
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