To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP, where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is related to the coord...

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...

The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence r...

in this note the notion of interval-valued fuzzy b-algebras (briefly,i-v fuzzy b-algebras), the level and strong level b-subalgebra is introduced.then we state and prove some theorems which determine the relationshipbetween these notions and b-subalgebras. the images and inverse images ofi-v fuzzy b-subalgebras are defined, and how the homomorphic images andinverse images of i-v fuzzy b-subalge...

In this paper, we introduce the concept of doubt intuitionistic fuzzy subalgebras and doubt intuitionistic fuzzy ideals in BCK/BCI-algebras. We show that an intuitionistic fuzzy subset of BCK/BCI-algebras is an intuitionistic fuzzy subalgebra and an intuitionistic fuzzy ideal if and only if the complement of this intuitionistic fuzzy subset is a doubt intuitionistic fuzzy subalgebra and a doubt...

We study the semisimplicity of category $KL_k$ for affine Lie superalgebras and provide a super analog certain results from arXiv:1801.09880. Let $KL_k^{fin}$ be subcategory consisting ordinary modules on which Cartan subalgebra acts semisimply. prove that is semisimple when 1) $k$ collapsing level, 2) $W_k(\mathfrak{g}, \theta)$ rational, 3) in category. The analysis subtler than algebra case,...

For the Kirillov–Poisson structure on the vector space g∗, where g is a finite-dimensional Lie algebra, it is known at least two canonical deformations quantization of this structure: they are the M.Kontsevich universal formula [K], and the formula, arising from the classical Campbell–Baker–Hausdorff formula [Ka]. It was proved in [Ka] that the last formula is exactly the part of Kontsevich’s f...

In this note the notion of interval-valued fuzzy B-algebras (briefly,i-v fuzzy B-algebras), the level and strong level B-subalgebra is introduced.Then we state and prove some theorems which determine the relationshipbetween these notions and B-subalgebras. The images and inverse images ofi-v fuzzy B-subalgebras are defined, and how the homomorphic images andinverse images of i-v fuzzy B-subalge...