相关论文: Building relativized representations using games
Building on work of Maltsev on locally free algebras in finite purely functional languages, we revisit the model theory of (absolutely free) term algebras and their completions. Maltsev's analysis yields a natural axiomatization together…
We introduce the notion of a generalized representation of a Jordan algebra with unit. The greneralized representation has the following properties: (1) Usual representations and Jacobson representations correspond to special cases of…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…
We assign a relational structure to any finite algebra in a canonical way, using solution sets of equations, and we prove that this relational structure is polymorphism-homogeneous if and only if the algebra itself is…
In recent work, Watanabe, Eberhart, Asada, and Hasuo have shown that parity games can be seen as string diagrams, that is, as the morphisms of a symmetric monoidal category, an algebraic structure with two different operations of…
This paper presents a universal representation of symmetric (permutation-invariant) functions with multidimensional variable-size variables. These representations help justify approximation methods that aggregate information from each…
We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we…
We observe that the group of all lifts of elements of Thompson's group $T$ to the real line is finitely presented and contains the additive group $\mathbb{Q}$ of the rational numbers. This gives an explicit realization of the Higman…
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…
The article is devoted to some ``strange'' phenomena of representation theory and their interrelations. Cross-projective representations of pairs of anticommutative algebras, alloys, their universal envelopping Lie algebras and their…
We introduce the notion of reflexivity for combinatory algebras. Reflexivity can be thought of as an equational counterpart of the Meyer-Scott axiom of combinatory models, which indeed allows us to characterise an equationally definable…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
Relative property (T) has recently been used to construct a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs…
Strategic games admit a multi-graph representation, in which two kinds of relations, accessibility, and preferences, are used to describe how the players compare the possible outcomes. A category of games with a fixed set of players…
We construct a De Morgan algebra-valued logic with quantifiers, where the truth values are in a finite De Morgan algebra, We show that there is a representation theorem of the cylindric algebra of this logic from which a completeness…
We give an overview of some of the main results in geometric representation theory that have been proved by means of the Steinberg variety. Steinberg's insight was to use such a variety of triples in order to prove a conjectured formula by…
Cohen and Taylor introduced Plesken Lie algebras of finite groups and studied their structural properties. As a further step, we will introduce Plesken Lie algebra representations, Plesken Lie algebra modules and discuss the irreducibility…
The representations of a $k$-graph $C^*$-algebra $C^*(\Lambda)$ which arise from $\Lambda$-semibranching function systems are closely linked to the dynamics of the $k$-graph $\Lambda$. In this paper, we undertake a systematic analysis of…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where…