相关论文: On simple and semisimple quantales
This work mainly concerns the -- here introduced -- category of $\mathscr Q$-sets and functional morphisms, where $\mathscr Q$ is a commutative semicartesian quantale. We describe, in detail, the limits and colimits of this complete and…
We introduce a minimalistic notion of semiclassical quantization and use it to prove that the convex hull of the semiclassical spectrum of a quantum system given by a collection of commuting operators converges to the convex hull of the…
Some filter relative notions of size, $\left( \mathcal{F},\mathcal{G}\right) $-syndeticity and piecewise $\mathcal{F} $-syndeticity, were defined and applied with clarity and focus by Shuungula, Zelenyuk and Zelenyuk in their paper ``The…
We give a comprehensive study of the so-called \textit{semi-tripotent rings} obtaining their new and non-trivial characterization as well as a complete description in terms of sums and products of some special elements. Particularly, we…
We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson showing that simple endotrivial modules of most groups come from…
In this paper we obtain several new complete characterizations of pseudolinear functions. Two of the results are of first-order and one is derivative free. All results are derived in terms of the Clarke-Rockafellar subdifferential.…
We provide a novel construction of quantized universal enveloping $*$-algebras of real semisimple Lie algebras, based on Letzter's theory of quantum symmetric pairs. We show that these structures can be `integrated', leading to a…
We survey mathematical properties of quasicrystals, first from the point of view of harmonic analysis, then from the point of view of morphic and automatic sequences. Nous proposons un tour d'horizon de propri\'et\'es math\'ematiques des…
Answering a question of Frank Calegari, we extend some of our earlier results on dimension of fixed point spaces of elements in irreducible linear groups. We consider characteristic polynomials rather than just fixed spaces.
Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination result for certain modules over finite simple extensions of the…
Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…
We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsemimodules and posets of splitting subsemimodules and…
We reconstruct finite-dimensional quantum theory from categorical principles. That is, we provide properties ensuring that a given physical theory described by a dagger compact category in which one may `discard' objects is equivalent to a…
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…
We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups. Several new quantum groups constructed by Banica, Curran and Speicher since the…
The notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…
In this paper we show how a theorem of Jantzen relating the character of a finite dimensional irreducible representation of a disconnected semisimple algebraic group on elements outside the connected component of identity to character of an…
A new pseudoclassical model to describe Weyl particles is proposed. Different ways of its quantization are presented. They all lead to the theory of Weyl particle; namely, the massless Dirac equation and the Weyl condition are reproduced.…
In this paper we give a new characterization of simple sets of polynomials B with the property that the set of B-multiplier sequences contains all Q-multiplier sequence for every simple set Q. We characterize sequences of real numbers which…
We substantially refine the theory of singular principal bundles introduced in a former paper. In particular, we show that we need only honest singular principal bundles in our compactification. These are objects which carry the structure…