Unitary Superalgebras Research Articles

Unitary superalgebras with graded involution or superinvolution of polynomial growth

In this paper we study associative unitary superalgebras with graded involution or superinvolution having polynomial growth of the codimension sequence. The first goal is to prove that, for this kind of algebras , the codimension sequence is a polynomial with rational coefficients. Then we shall construct several superalgebras with graded involution or superinvolution realizing the smallest and the largest value of the leading term of such a polynomial.

Super-Hubbard models and applications

We construct XX- and Hubbard- like models based on unitary superalgebras gl(N|M) generalising Shastry's and Maassarani's approach of the algebraic case. We introduce the R-matrix of the gl(N|M) XX model and that of the Hubbard model defined by coupling two independent XX models. In both cases, we show that the R-matrices satisfy the Yang--Baxter equation, we derive the corresponding local Hamiltonian in the transfer matrix formalism and we determine the symmetry of the Hamiltonian. Explicit examples are worked out. In the cases of the gl(1|2) and gl(2|2) Hubbard models, a perturbative calculation at two loops a la Klein and Seitz is performed.

Hermitean Oscillator‐like Realizations of Classical Algebras and Superalgebras in Hilbert Space with Positive Definite Metric

AbstractThe hermitean oscillator‐like realizations of classical algebras in terms of bosonic and fermionic creation and annihilation operators are given. The hermitean realizations of classical superalgebras using boson‐fermion oscillators are explicitely described. The assumption of positive definite metric in a Hilbert space of the oscillators states is exploited. Due to this fact, the realizations of superalgebras in the Hilbert space can be constructed only for: the real orthosymplectic superalgebra osp (N; 2M; R); the unitary compact superalgebra su (N; M); the unitary noncompact one SU(N; K, M); and the quaternionic unitary superalgebra uuα(N; M; H).