124,616 research outputs found
Quasitriangularity and enveloping algebras for inhomogeneous quantum groups
Coquasitriangular universal matrices on quantum Lorentz and
quantum Poincar\'e groups are classified. The results extend (under certain
assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on
those objects are described.Comment: 18 pages, LaTeX file, minor change
The Dirac operator and gamma matrices for quantum Minkowski spaces
Gamma matrices for quantum Minkowski spaces are found. The invariance of the
corresponding Dirac operator is proven. We introduce momenta for spin 1/2
particles and get (in certain cases) formal solutions of the Dirac equation.Comment: 25 pages, LaTeX fil
Modular and lower-modular elements of lattices of semigroup varieties
The paper contains three main results. First, we show that if a commutative
semigroup variety is a modular element of the lattice Com of all commutative
semigroup varieties then it is either the variety COM of all commutative
semigroups or a nil-variety or the join of a nil-variety with the variety of
semilattices. Second, we prove that if a commutative nil-variety is a modular
element of Com then it may be given within COM by 0-reduced and substitutive
identities only. Third, we completely classify all lower-modular elements of
Com. As a corollary, we prove that an element of Com is modular whenever it is
lower-modular. All these results are precise analogues of results concerning
modular and lower-modular elements of the lattice of all semigroup varieties
obtained earlier by Jezek, McKenzie, Vernikov, and the author. As an
application of a technique developed in this paper, we provide new proofs of
the `prototypes' of the first and the third our results.Comment: 15 page
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