First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type Bn), under the assumption that the order of the group is invertible in the base field. Special case of the result is a finite presentation of the algebra of multisymmetric polynomials. Reducedness of the invariant commuting scheme is proved as a by-...

We study Thurston’s norm on the second homology of a 3-manifold. The novelty of our approach consists in the use of methods of the C∗algebra theory. Namely, for Stallings’ fibration M with pseudo-Anosov monodromy, we associate a C∗-algebra whose K-theory gives rise to an algebraic number field K. We show that the trace function on the ring of integers of K induces a norm on the second homology ...

Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces real forms of complex algebras, are well-studied in the context symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely, introduce concept pseudo-involution, an automorphism which is only required act involutively on stable Cartan subalgebra, pseudo-fixed-point natural substitute fo...

The task to construct parametrices of elliptic differential operators on a manifold with edges requires a calculus of operators with a two-component principal symbolic hierarchy, consisting of (edge-degenerate) interior and (operator-valued) edge symbols. This so-called edge-algebra can be interpreted as a generalisation of the (pseudo-differential) algebra of boundary value problems without th...

Schematic su(2)⊕ h3 interaction Hamiltonians, where su(2) plays the role of the pseudo-spin algebra of fermion operators and h3 is the Heisenberg algebra for bosons, are shown to be closely related to certain nonlinear models defined on a single quantum algebra suq(2) of quasifermions. In particular, suq(2) analogues of the Da ProvidenciaSchütte and extended Lipkin models are presented. The con...

Forest algebras are defined for investigating languages of forests [ordered sequences] of unranked trees, where a node may have more than two [ordered] successors [9]. We show that several parameters on forests can be realized as forest algebra homomorphisms from the free forest algebra into algebras which retain the equational axioms of forest algebras. This includes the number of nodes, the n...

In this paper, we deal with the invertible elements in a complete intuitionistic fuzzy pseudo normed algebra (in short, IFPNA) respect to Archimedean t-norm and t-conorm. It is done by studying continuity of algebraic operations IFPNA investigating condition for existence inverse an element IFPNA. Also some properties are studied. observed that set open set.

In a recent paper pair of operators $a$ and $b$ satisfying the equations $a^\dagger a=bb^\dagger+\gamma\1$ $aa^\dagger=b^\dagger b+\delta\1$, has been considered, their nature ladder deduced analysed. Here, motivated by spreading interest in non self-adjoint Quantum Mechanics, we extend this situation to set four operators, $c$, $d$, $r$ $s$, $ dc=rs+\gamma\1$ $cd=sr+\delta\1$, show that they a...