Search results for "General linear group"
showing 4 items of 4 documents
Defining relations of minimal degree of the trace algebra of 3×3 matrices
2008
Abstract The trace algebra C n d over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n , d ⩾ 2 . Minimal sets of generators of C n d are known for n = 2 and n = 3 for any d as well as for n = 4 and n = 5 and d = 2 . The defining relations between the generators are found for n = 2 and any d and for n = 3 , d = 2 only. Starting with the generating set of C 3 d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C 3 d is equal to 7 for any d ⩾ 3 . We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8. The proofs are based …
A candidate for a noncompact quantum group
1996
A previous letter (Bidegain, F. and Pinczon, G:Lett. Math. Phys.33 (1995), 231–240) established that the star-product approach of a quantum group introduced by Bonneau et al. can be extended to a connected locally compact semisimple real Lie group. The aim of the present Letter is to give an example of what a noncompact quantum group could be. From half of the discrete series ofSL(2,\(\mathbb{R}\)), a new type of quantum group is explicitly constructed.
Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group or a Unitary Group
2001
We construct some divisible designs starting from a projective space. These divisible designs admit an orthogonal group or a unitary group as an automorphism group.
Determinant Bundles over Grassmannians
1989
Denoting by H the Hilbert space of square-integrable Dirac spinor fields on a manifold M, transforming according to a unitary representation p of a gauge group G, we have a linear representation of the group g of gauge transformations in the space H. If ρ is faithful we can consider g as a subgroup of the general linear group GL(H). By constructing representations of GL(H) we automatically obtain representations of g. It turns out that in the case when the dimension d of M is odd, g is contained in a smaller group GLp ⊂ GL(H) which has the property that it perturbs the subspace H+ ⊂ H consisting of eigenvectors of a Dirac operator belonging to positive eigenvalues, by an operator A for whic…