#20029: Implement quantum matrix coordinate algebras
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_work
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|
087245c395b4d6b3f0f9b53e5e77100121c9bce1
Dependencies: | Stopgaps:
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Changes (by tscrim):
* status: needs_review => needs_work
Comment:
I've added a class for GL,,q,,(n), but it currently fails the antipode
test. I've also changed the convention from `q^2` to `q`. I just ran
another test and it says that it is failing associativity, so the bug is
probably in the multiplication code.
However, can you check to make sure the following data is correct?
{{{
sage: O = algebras.QuantumGL(2)
sage: O.quantum_determinant()
x[1,1]*x[2,2] - q*x[1,2]*x[2,1]
sage: for g in O.algebra_generators():
....: print "{:>8}{:>33}{:>35}{:>2}".format(g, g.antipode(),
....: g.coproduct(), g.counit())
x[1,1] c*x[2,2] x[1,1] # x[1,1] + x[1,2] #
x[2,1] 1
x[1,2] -(q^-1)*c*x[2,1] x[1,1] # x[1,2] + x[1,2] #
x[2,2] 0
x[2,1] -q*c*x[1,2] x[2,1] # x[1,1] + x[2,2] #
x[2,1] 0
x[2,2] c*x[1,1] x[2,1] # x[1,2] + x[2,2] #
x[2,2] 1
c x[1,1]*x[2,2] - q*x[1,2]*x[2,1] c #
c 1
}}}
This agrees with Valentin's paper if `c = 1`.
--
Ticket URL: <http://trac.sagemath.org/ticket/20029#comment:15>
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