Related papers: Reflexive tactics for algebra, revisited
We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
We give an algebro-geometric classification of smooth real affine algebraic surfaces endowed with an effective action of the real algebraic circle group $\mathbb{S}^1$ up to equivariant isomorphisms. As an application, we show that every…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
In [LWY23] the authors construct the reflective center of a module category M over a braided monoidal category B. The reflective center is by construction a braided module category over B. In the case where B is the category of modules over…
We consider algebras of languages over the signature of reversible Kleene lattices, that is the regular operations (empty and unit languages, union, concatenation and Kleene star) together with intersection and mirror image. We provide a…
We consider the reflection equation algebra for a finite dimensional R-matrix for the $(h,w)$-deformed Heisenberg algebra ${\cal U}_{h,w}(h(4))$. A representation of the reflection matrix $K$ is constructed using the matrix generators…
We propose various methods for combining or amalgamating propositional languages and deductive systems. We make heavy use of quantales and quantale modules in the wake of previous works by the present and other authors. We also describe…
We express the defining relations of the $q$-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties…
Drinfeld twists, and the twists of Giaquinto and Zhang, allow for algebras and their modules to be deformed by a cocycle. We prove general results about cocycle twists of algebra factorisations and induced representations and apply them to…
Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…
Let $\mathfrak{g}$ be a compact simple Lie algebra. We modify the quantized enveloping $^*$-algebra associated to $\mathfrak{g}$ by a real-valued character on the positive part of the root lattice. We study the ensuing Verma module theory,…
The aim of the paper is twofold. First, we introduce analogs of (partial) derivatives on certain Noncommutative algebras, including some enveloping algebras and their "braided counterparts", namely, the so-called modified Reflection…
Flipped classroom pedagogy is widely used in undergraduate mathematics to promote active learning, yet it remains unclear whether students experience it in systematically different ways. In this study, we analyze student perceptions from an…
A ``Wick rotation'' is applied to the noncommutative sphere to produce a noncommutative version of the hyperboloids. A harmonic basis of the associated algebra is given. It is noted that, for the one sheeted hyperboloid, the vector space…
Gelfand's trick shows that the spherical Hecke algebra of a $p$-adic split reductive group is commutative. We adapt this strategy in order to show that the spherical derived Hecke algebra is graded-commutative under mild assumptions on the…
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
We give a new formulation of Turing reducibility in terms of higher modalities, inspired by an embedding of the Turing degrees in the lattice of subtoposes of the effective topos discovered by Hyland. In this definition, higher modalities…
In this paper, we study partitions of finite modules induced by rank support and rank weight. First, we show that partitions induced by rank support are mutually dual with respect to suitable non-degenerate pairings, and hence are…