We compute the Hilbert series of graded algebra real regular functions on a linear symplectic quotient by 2-torus as well first four coefficients Laurent expansion this at $$t = 1$$ . describe an algorithm to in explicit examples.

EQ-algebras were introduced by Nov?ak in [16] as an algebraic structure of truth values for fuzzy type theory (FTT). Nov?k and De Baets [18] various kinds such good, residuated, lattice ordered EQ-algebras. In any logical structures, using filters, one can construct other structures. With this inspirations, means fantastic filters we MV-algebras. Also, study prelinear introduce a new kind filte...

In this paper, we generalize the notion of border bases of zerodimensional polynomial ideals to the module setting. To this end, we introduce order modules as a generalization of order ideals and module border bases of submodules with finite codimension in a free module as a generalization of border bases of zero-dimensional ideals in the first part of this paper. In particular, we extend the d...

In this paper we solve moment problems for Poisson transforms and, more generally, for completely positive linear maps on unital C∗-algebras generated by “universal” row contractions associated with F+n , the free semigroup with n generators. This class of C ∗-algebras includes the Cuntz-Toeplitz algebra C∗(S1, . . . , Sn) (resp. C ∗(B1, . . . , Bn)) generated by the creation operators on the f...

It is shown that $A:=H_{1,\eta}(G)$, the Sympectic Reflection Algebra, has $T_G$ independent traces, where number of conjugacy classes elements without eigenvalue 1 belonging to finite group $G$ generated by system symplectic reflections. Simultaneously, we show algebra $A$, considered as a superalgebra with natural parity, $S_G$ supertraces, -1 $G$. We consider also $A$ Lie $A^L$ and $A^S$. if...

We introduce the notion of an adequate moduli space. The theory of adequate moduli spaces provides a framework for studying algebraic spaces which geometrically approximate algebraic stacks with reductive stabilizers in characteristic p. The definition of an adequate moduli space generalizes the existing notion of a good moduli space to characteristic p (and mixed characteristic). The most impo...

A closed subgroup H of the affine, algebraic group G is called observable if G/H is a quasi-affine algebraic variety. In this paper we define the notion of an observable subgroup of the affine, algebraic monoid M . We prove that a subgroup H of G is observable in M if and only if H is closed in M and there are “enough” H-semiinvariant functions in k[M ]. We show also that a closed, normal subgr...

Motivated by the relation between Schur algebra and group of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang Steffen Koenig [15], [16] addressed some behaviour endomorphism generator over algebra, which they called gendo-symmetric algebra. Continuing this line works, we classify article representation-finite algebras that have precisely one isomorphism cla...

In the present paper, we introduce a class of infinite Lie conformal superalgebras S(p), which are closely related to algebras extended Block type defined in [6]. Then all finite non-trivial irreducible modules over S(p) for p?C? completely classified. As an application, also classifications quotient s(n) n?1 and sh is isomorphic subalgebra algebra N=2 superconformal algebra. Moreover, as gener...

Algebra extensions A ⊆ B where A is a left B-module such that the Baction extends the multiplication in A are ubiquitous. We encounter examples of such extensions in the study of group actions, group gradings or more general Hopf actions as well as in the study of the bimodule structure of an algebra. In this paper we are extending R.Wisbauer’s method of constructing the central closure of a se...