Given a star product with separation of variables ⋆ on pseudo-Kähler manifold M and point x0∈M, we construct an associative algebra formal distributions supported at x0. We use this to express the oscillatory exponents family integrals related ⋆.

The notion of vague ideals in pseudo MV-algebras is introduced,and several properties are investigated. Conditions for a vague set to be avague ideal are provided. Conditions for a vague ideal to be implicative aregiven. Characterizations of (implicative, prime) vague ideals are discussed.The smallest vague ideal containing a given vague set is established. Primeand implicative extension proper...

Let $G$ be a split connected reductive group over finite field of characteristic $p > 2$ such that $G_\text{der}$ is absolutely almost simple. We give geometric construction perverse $\mathbb{F}_p$-sheaves on the Iwahori affine flag variety which are central with respect to convolution product. deduce an explicit formula for isomorphism from spherical mod $p$ Hecke algebra center algebra. also ...

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on $Aoplus X$ and generalize the module extension Banach algebras. We  obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.

A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it can be embedded as an order ideal in its so-called unitization, which does have a unit. We study unitizations of GPEAs with respect to a unitizing automorphi...

Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. Then ${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$ becomes a module extension Banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on ${mathcal{S...

Via the introduction of (infinitary) disjunctions on any complete lattice while inheriting the meet as a conjunction, we construct a bijective correspondence (up to isomorphism) between complete lattices L and complete Heyting algebras DI(L) equipped with a so called disjunctive join dense closure operator RL. If L is itself a complete Heyting algebra then DI(L) ∼= L and RL = idDI(L). Ortholatt...

We show that the Lorentz covariant formulation of N = 2 string in a curved space reveals an explicit hyper–Kähler structure. Apart from the metric, the superconformal currents couple to a background two–form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra. P...

Pseudo-Galois extensions are shown to be depth two extensions. Studying its left bialgebroid, we construct an enveloping Hopf algebroid for the semi-direct product of groups or involutive Hopf algebras and their module algebras. It is a type of cofibered sum of two inclusions of the Hopf algebra into the semi-direct product and its derived right crossed product. Van Oystaeyen and Panaite observ...