100 research outputs found
Irreducible completely pointed modules of quantum groups of type
We give a classification of all irreducible completely pointed
modules over a characteristic zero field in which
is not a root of unity. This generalizes the classification result of
Benkart, Britten and Lemire in the non quantum case. We also show that any
infinite-dimensional irreducible completely pointed
can be obtained from some irreducible completely pointed module over the
quantized Weyl algebra .Comment: 25 page
Change of the *congruence canonical form of 2-by-2 matrices under perturbations
We study how small perturbations of a 2-by-2 complex matrix can change its
canonical form for *congruence. We construct the Hasse diagram for the closure
ordering on the set of *congruence classes of 2-by-2 matrices.Comment: 8 pages. arXiv admin note: substantial text overlap with
arXiv:1105.216
Roth’s solvability criteria for the matrix equations AX - XB^ = C and X - AXB^ = C over the skew field of quaternions with aninvolutive automorphism q ¿ qˆ
The matrix equation AX-XB = C has a solution if and only if the matrices A C 0 B and A 0
0 B are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988) proved that the matrix equation X - AXB = C over a field has a solution if and only if the matrices A C 0 I and I 0 0 B are simultaneously equivalent to A 0 0 I and
I 0 0 B . We extend these criteria to the matrix equations AX- ^ XB = C and X - A ^ XB = C over the skew field of quaternions with a fixed involutive automorphism q ¿ ˆq.Postprint (author's final draft
Rings of invariants of finite groups when the bad primes exist
Let R be a ring (not necessarily with 1) and G be a finite group of automorphisms of R. The set B(R, G) of primes p such that p | |G| and R is not p-torsion free, is called the set of bad primes. When the ring is |G|-torsion free, i.e., B(R, G) is empty set, the properties of the rings R and R^G are closely connected. The aim of the paper is to show that this is also true when B(R, G) is not empty set under natural conditions on bad primes. In particular, it is shown that the Jacobson radical (resp., the prime radical) of the ring R^G is equal to the intersection of the Jacobson radical (resp., the prime radical) of R with R^G; if the ring R is semiprime then so is R^G; if the trace of the ring R is nilpotent then the ring itself is nilpotent; if R is a semiprime ring then R is left Goldie iff the ring R^G is so, and in this case, the ring of G-invariants of the left quotient ring of R is isomorphic to the left quotient ring of R^G and
im (R^G)\leq
im (R)\leq |G|
im (R^G)
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