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A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
The article is devoted to the investigation of representation of rational numbers by Cantor series. Necessary and sufficient conditions for a rational number to be representable by a positive Cantor series are formulated for the case of an…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
Let $A$ be an additively cancellative semialgebra over an additively cancellative semifield $K$ as defined in [9]. For a given partial action $\alpha$ of a group $G$ on an algebra, the associativity of partial skew group ring together with…
Possibility theory offers either a qualitive, or a numerical framework for representing uncertainty, in terms of dual measures of possibility and necessity. This leads to the existence of two kinds of possibilistic causal graphs where the…
We construct quasi-Hopf algebras associated with a semisimple Lie algebra, a complex curve and a rational differential. This generalizes our previous joint work with V. Rubtsov (Israel J. Math. (1999) and q-alg/9608005).
This is a write-up of the discussions during the meetings of the study group on representation theory of semirings which was organized at the Department of Mathematics, Uppsala University, during the academic year 2017-2018. The main…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
Study designs classified as quasi- or natural experiments are typically accorded more face validity than observational study designs more broadly. However, there is ambiguity in the literature about what qualifies as a quasi-experiment.…
We present in an informal way some recent results concerning a possible overlapping between classical unpredictability and quantum indeterminism.
We survey recent developments on rationality problems for algebraic varieties, with a particular emphasis on cycle-theoretic and combinatorial methods and their applications to hypersurfaces.
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
We prove the conjecture of Kac-Wakimoto on the rationality of exceptional W-algebras for the first non-trivial series, namely, for the Bershadsky-Polyakov vertex algebras $W_3^{(2)}$ at level $k=p/2-3$ with $p=3,5,7,...$. This gives new…
Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their…
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…
Many decision-making scenarios, e.g., public policy, healthcare, business, and disaster response, require accommodating the preferences of multiple stakeholders. We offer the first formal treatment of reasoning with multi-stakeholder…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more…
The notion of relative cuspidality for distinguished representations attached to $p$-adic symmetric spaces is introduced. A characterization of relative cuspidality in terms of Jacquet modules is given and a generalization of Jacquet's…
In previous work, the authors introduced the notion of Q-Koszul algebras, as a tool to "model" module categories for semisimple algebraic groups over fields of large characteristics. Here we suggest the model extends to small…