Related papers: Strong duality Data of type $A$ and extended $T$-s…
We introduce a notion of strong periodicity of a module over a finite-dimensional algebra over a field. We prove that the existence of such modules over certain idempotent algebras is both a necessary and sufficient condition for the…
The classical duality theory associates to an abelian group a dual companion. Passing to a non-abelian group, a dual object can still be defined, but it is no longer a group. The search for a broader category which should include both the…
We continue the theory of $\tT$-systems from the work of the second author, describing both ground systems and module systems over a ground system (paralleling the theory of modules over an algebra). The theory, summarized categorically at…
We extend a duality theorem of Schneider-Stuhler about $Ext^i[\pi_1,\pi_2]$ proved there for smooth representations of a $p$-adic group $G$ with central characters to all smooth representations assuming their result for only irreducible…
In extended hearts of bounded $t$-structures on a triangulated category, we provide a Happel-Reiten-Smalo tilting theorem and a characterization for $s$-torsion pairs. Applying these to $m$-extended module categories, we characterize…
We prove a Tannaka duality theorem for $(\infty,1)$-categories. This is a duality between certain derived group stacks, or more generally certain derived gerbes, and symmetric monoidal $(\infty,1)$-categories endowed with particular…
Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…
We show that the discrete-time evolution of an open quantum system generated by a single quantum channel $T$ can be embedded in the discrete-time evolution of an enlarged closed quantum system, i.e. we construct a unitary dilation of the…
Let $Y$ denote a $D$-class symmetric association scheme with $D \geq 3$, and suppose $Y$ is almost-bipartite P- and Q-polynomial. Let $x$ denote a vertex of $Y$ and let $T=T(x)$ denote the corresponding Terwilliger algebra. We prove that…
We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded conformal vertex algebra under suitable…
F.~Schweiger introduced the fibred system in \cite{Schweiger-MCF}, to unify and generalize many known continued fraction algorithms. An advantage of a fibred system is that it often provides a systematic construction of absolutely…
We generalize the idea of "extension of Hamiltonian systems" -- developed in a series of previous articles -- which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of…
In the paper [1] we showed that in double space, where all initial coordinates $x^\mu$ are doubled $x^\mu \to y_\mu$, the T-duality transformations can be performed by exchanging places of some coordinates $x^a$ and corresponding dual…
We incorporate strong negation in the theory of computable functionals TCF, a common extension of Plotkin's PCF and G\"{o}del's system $\mathbf{T}$, by defining simultaneously strong negation $A^{\mathbf{N}}$ of a formula $A$ and strong…
In this paper, we obtain some new results on the existence of MDS self-dual codes utilizing (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. For some fixed $q$, our results can produce more classes of MDS…
We introduce a self-dual field strength which replaces the gauge field in spontaneously broken Yang-Mills theory, reformulating it as a Lorentz covariant non-linear sigma model. This dualized theory is in both a unitary and renormalizable…
We introduce the notion of K-theoretic duality for extensions of separable unital nuclear $C^*$-algebras by using K-homology long exact sequence and cyclic six term exact sequence for K-theory groups of extensions. We then prove that the…
We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSI's. The recently introduced duality on SSI's is given an effective conceptual and computational setting. We study strongly…
We extend the covariant color-kinematics duality introduced by Cheung and Mangan to effective field theories. We focus in particular on relations between the effective field theories of gluons only and of gluons coupled to bi-adjoint…
A general and systematic construction of Non Abelian affine Toda models and its symmetries is proposed in terms of its underlying Lie algebraic structure. It is also shown that such class of two dimensional integrable models naturally leads…