For symplectic Lie algebras sp(2n,C), denote by b and n its Borel subalgebra and maximal nilpotent subalgebra, respectively. We construct a relationship between the abelian ideals of b and the cohomology of n with trivial coefficients. By this relationship, we can enumerate the number of abelian ideals of b with certain dimension via the Poincaré polynomials of Weyl groups of type An−1 and Cn.

We establish branching rules between some Iwahori-Hecke algebra of type B and their subalgebras which are defined as fixed subalgebras by involutions including Goldman involution. The IwahoriHecke algebra of type D is one of such fixed subalgebras. We also obtain branching rules between those fixed subalgebras and their intersection subalgebra. We determine basic sets of irreducible representat...

A new quantum deformation, which we call null-plane, of the (3+1) Poincaré algebra is obtained. The algebraic properties of the classical null-plane description are generalized to this quantum deformation. In particular, the classical isotopy subalgebra of the null-plane is deformed into a Hopf subalgebra, and deformed spin operators having classical commutation rules can be defined. Quantum Ha...

Abstract. A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a “canonical basis” for every finite dimensional irreducible Uq(sl(n))-module. It is also shown that the algebra of functions on any quantum homogeneous space is generated by quan...

We analyze the decomposition of the enveloping algebra of the conformal algebra in arbitrary dimension with respect to the mass-squared operator. It emerges that the subalgebra that commutes with the mass-squared is generated by its Poincaré subalgebra together with a vector operator. The special cases of the conformal algebras of two and three dimensions are described in detail, including the ...

We present a new algorithm for computing a SAGBI basis up to an arbitrary degree for a subalgebra generated by a set of homogeneous polynomials. Our idea is based on linear algebra methods which cause a low level of complexity and computational cost. We then use it to solve the membership problem in subalgebras.

We analyze the decomposition of the enveloping algebra of the conformal algebra in arbitrary dimension with respect to the mass-squared operator. It emerges that the subalgebra that commutes with the mass-squared is generated by its Poincaré subalgebra together with a vector operator. The special cases of the conformal algebras of two and three dimensions are described in detail, including the ...

The orbits of Weyl groups W (An) of simple An type Lie algebras are reduced to the union of orbits of the Weyl groups of maximal reductive subalgebras of An. Matrices transforming points of the orbits of W (An) into points of subalgebra orbits are listed for all cases n ≤ 8 and for the infinite series of algebra-subalgebra pairs An ⊃ An−k−1 × Ak × U1, A2n ⊃ Bn, A2n−1 ⊃ Cn, A2n−1 ⊃ Dn. Numerous ...

In order to describe non-Hamiltonian (dissipative) systems in quantum theory we need to use non-Lie algebra such that commutators of this algebra generate Lie subalgebra. It was shown that classical connection between analytic group (Lie group) and Lie algebra, proved by Lie theorems, exists between analytic loop, commutant of which is associative subloop (group), and commutant Lie algebra (an ...

Patras, Reutenauer (J. Algebr. Comb. 16:301–314, 2002) describe a subalgebra A of the Malvenuto-Reutenauer algebra P . Their paper contains several characteristic properties of this subalgebra. In an unpublished manuscript Manfred Schocker states without proof a theorem, providing two further characterizations of the Patras-Reutenauer algebra. In this paper we establish a slightly generalized v...