Let Σ be a closed, orientable surface of genus g. It is known that the SU(2, 1) representation variety of π1(Σ) has 2g− 3 components of (real) dimension 16g− 16 and two components of dimension 8g−6. Of special interest are the totally loxodromic, faithful (that is quasi-Fuchsian) representations. In this paper we give global real analytic coordinates on a subset of the representation variety th...

We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of a state, its dynamical evolution rule and another rather trivial postulate proposed here (Read-Off Postulate). The wave function collapse and the probabilit...

The Lawrence-Krammer representation of the braid groups recently came to prominence when it was shown to be faithful by myself and Krammer. It is an action of the braid group on a certain homology module H2(C̃) over the ring of Laurent polynomials in q and t . In this paper we describe some surfaces in C̃ representing elements of homology. We use these to give a new proof that H2(C̃) is a free mod...

The minimal degree of an inverse semigroup S is the minimal cardinality of a set A such that S is isomorphic to an inverse semigroup of one-to-one partial transformations of A . The main result is a formula that expresses the minimal degree of a finite inverse semigroup S in terms of certain subgroups and the ordered structure of S . In fact, a representation of S by one-to-one partial transfor...

Gabriele Contessa In this paper, I develop Mauricio Suárez’s distinction between denotation, epistemic representation, and faithful epistemic representation. I then outline an interpretational account of epistemic representation, according to which a vehicle represents a target for a certain user if and only if the user adopts an interpretation of the vehicle in terms of the target, which would...

In this paper we give criteria for an ideal J of a TAF algebra A to be meet irreducible. We show that J is meet irreducible if and only if the C∗-envelope of A/J is primitive. In that case, A/J admits a faithful nest representation which extends to a ∗-representation of the C∗-envelope for A/J . We also characterize the meet irreducible ideals as the kernels of bounded nest representations; thi...

Let H be a finite Hopf C*-algebra and A of dimension. In this paper, we focus on the crossed product A⋊H arising from action A, which is ∗-algebra. terms faithful positive Haar measure C*-algebra, one can construct linear functional ∗-algebra A⋊H, further functional. Here, complete positivity plays vital role in argument. At last, conclude that dimension according to ∗- representation.

We use the gluing construction introduced by Jia Huang to explore rings of invariants for a range modular representations. construct generating sets maximal parabolic subgroups finite symplectic group and their common Sylow p -subgroup. also investigate singular classical groups. introduce this compute invariant field fractions thin faithful representations semidirect products determine minimum...

We show a complete classification of faithful representations the 2 + 1 space-times Galilean Lie algebra on polynomial ring in three variables, where actions are given by derivations with coefficients degree at most one. In particular, all such explicitly constructed and classified one parameter. more general setting we that, respect to nonzero abelian ideal finite-dimensional algebra, there is...