Related papers: Generalized Goulden-Yong duals and signed minimal …
In this paper we use a generalized vector product to construct an exterior form $\wedge :(\mathbb{R}^{n}) ^{k}\to \mathbb{R}^{\binom{n}{k}}$, where $\binom{n}{k}=\frac{n!}{(n-k)!k!}$, $k\leq n$. Finally, for $n=k-1$ we introduce the…
We consider the quiver Yangians associated to general affine Dynkin diagrams. Although the quivers are generically not toric, the algebras have some similar structures. The odd reflections of the affine Dynkin diagrams should correspond to…
The construction elements of the factorised form of the Yang-Baxter R operator acting on generic representations of q-deformed sl(n+1) are studied. We rely on the iterative construction of such representations by the restricted class of…
In this article, we construct explicit examples of pairs of non-isomorphic trees with the same restricted $U$-polynomial for every $k$; by this we mean that the polynomials agree on terms with degree at most $k+1$. The main tool for this…
We apply the notion of relative adjoint functor to generalise closed monoidal categories. We define representations in such categories and give their relation with left actions of monoids. The translation of these representations under lax…
We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and…
We calculate the partition function of the $SU(N)$ ( and $U(N)$) generalized $YM_2$ theory defined on an arbitrary Riemann surface. The result which is expressed as a sum over irreducible representations generalizes the Rusakov formula for…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
Jordan Normal Forms serve as excellent representatives of conjugacy classes of matrices over closed fields. Once we knows normal forms, we can compute functions of matrices, their main invariant, etc. The situation is much more complicated…
We develop a compositional framework for generalized reversible computing using copy-discard categories and resource theories. We introduce partitioned matrices between partitioned sets as subdistribution matrices which preserve the…
Generalized diagonal matrices are matrices that have two ladders of entries that are zero in the upper right and bottom left corners. The minors of generic generalized diagonal matrices have square-free initial ideals. We give a description…
Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…
In "A note on generalized Clifford algebras and representations" (Caenepeel, S.; Van Oystaeyen, F., Comm. Algebra 17 (1989) no. 1, 93--102.) generalized Clifford algebras were introduced via Clifford representations; these correspond to…
We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum $G_2$ manifolds. For a given $G_2$ manifold, we discuss evidence for the existence of mirror symmetries of two kinds:…
Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) of the generalized 2D Yang-Mills theories in the Schwinger--Fock gauge. Our calculation is done for arbitrary 2D…
An algebraic formalism, developped with V. Glaser and R. Stora for the study of the generalized retarded functions of quantum field theory, is used to prove a factorization theorem which provides a complete description of the generalized…
We study a secondary construction of Boolean functions, which generalizes the direct sum and the indirect sum. We detail how these two classic secondary constructions are particular cases of this more general one, as well as two known…
The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring $\mathcal{R}$ with a unit…
We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…
We present new generalized Cline's formula and Jacobson's lemma for the g-Drazin inverse in a ring. These extend many known results, e.g., Chen and Abdolyousefi (Generalized Jacobson's Lemma in a Banach algebra, Comm. Algebra, {\bf…