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We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory…
In this paper we study the notion of configuration for group actions. It is proved that some properties concerning configuration of groups can be extended for the case of group actions. The relationship between configuration and different…
In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.
Preface (A.Vershik) - about these texts (3.); I.Interpolation between inductive and projective limits of finite groups with applicatons to linear groups over finite fields; II.The characters of the groups of almost triangle matrices over…
In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of…
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…
We first consider the rational Cherednik algebra corresponding to the action of a finite group on a complex variety, as defined by Etingof. We define a category of representations of this algebra which is analogous to "category O" for the…
We study $\mathbb{R}^k \times \mathbb{Z}^\ell$ actions on arbitrary compact manifolds with a projectively dense set of Anosov elements and 1-dimensional coarse Lyapunov foliations. Such actions are called totally Cartan actions. We…
It is well known(cf. Weil, G\'erardin's works) that there are two different Weil representations of a symplectic group over an odd finite field. By a twisted action, we show that one can reorganize them as a representation of a related…
We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the…
In this paper we prove the tail variational principle for actions of countable amenable groups. This allows us to extend some characterizations of asymptotic $h$-expansiveness from $\mathbb{Z}$-actions to actions of countable amenable…
We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category. Additionally, we establish…
The class of Parikh word representable graphs were recently introduced. In this work, we further develop its general theory beyond the binary alphabet. Our main result shows that this class is equivalent to the class of bipartite…
Our goal is to classify all generically transitive actions of commutative unipotent groups on flag varieties up to conjugation. We establish relationship between this problem and classification of multiplications with certain properties on…
Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as…
We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for…
We describe simply connected compact exceptional simple Lie groups in very elementary way. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms of G, and determine…
We extend the notion of Novikov-Shubin invariant for free G-CW-complexes of finite type to spaces with arbitrary G-actions and prove some statements about their positivity. In particular we apply this to classifying spaces of discrete…
I provide several natural properties of group actions which translate into fragments of axiom of choice in the associated permutation models of choiceless set theory.
We describe the quantum cohomology rings of a class of toric varieties. The description includes, in addition to the (already known) ring presentations, the (new) analogues for toric varieties of the sorts of quantum Giambelli formulas…