We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. LetM denote a Bose-Mesner algebra on a finite nonempty set X . Fix p ∈ X , and letM∗ and T denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra ofMwith respect to p. By a hyper-duality ofM, we mean an automorphism ψ of T such that ψ(M) =M∗, ψ(M∗) =M; ψ2(A) = ...

A polyhedron is a graph G which simple, planar and 3-connected. In this note, we classify the family of strongly involutive self-dual polyhedra. The latter done by using well-known result due to Tutte characterizing 3-connected graphs. We also show that special class polyhedra self-duality behaves topologically as antipodal mapping. These are related with several problems in convex discrete geo...

In this paper, we study the relation between m-strongly Gorenstein projective (resp. injective) modules and n-strongly Gorenstein projective (resp. injective) modules whenever m 6= n, and the homological behavior of n-strongly Gorenstein projective (resp. injective) modules. We introduce the notion of n-strongly Gorenstein flat modules. Then we study the homological behavior of n-strongly Goren...

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras U?(su(2,2)?T4) and U?¯(su(2,2)?T¯4), where T4 describes complex twistor coordinates T¯4 dual momenta. The are suitably chosen as quantum-covariant modules (NC representations) Born-dual algebras. Subsequently, we introduce defor...

In this article we show that all periods of uniformizable $t$-modules (resp. their coordinates) can be obtained via specializing a rigid analytic trivialization related dual $t$-motive at $t=\theta$. The proof is even constructive. central object in the construction subset $H$ Tate algebra points $E$ which turns out to isomorphic period lattice kind generating series one direction and residues ...

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studyi...