ﻻ يوجد ملخص باللغة العربية
Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $pi^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${cal D} subset {cal H}$. Then we present several ways of extending $pi^o$, by closure, to some larger quasi *-algebra contained in $A$, either by Hilbert space operators, or by sesquilinear forms on ${cal D}$. Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.
In this thesis new objects to the existing set of invariants of Lie algebras are added. These invariant characteristics are capable of describing the nilpotent parametric continuum of Lie algebras. The properties of these invariants, in view of possi
Rota-Baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics. Rota-Baxter algebras provide a construction of pre-Lie algebras from associative algebras
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants (generalized Casimir operators) are found for three classes of Lie
We study the problem of classification of triples ($mathfrak{g}, f, k$), where $mathfrak{g}$ is a simple Lie algebra, $f$ its nilpotent element and $k in CC$, for which the simple $W$-algebra $W_k (mathfrak{g}, f)$ is rational.
The Minkowski spacetime quantum Clifford algebra structure associated with the conformal group and the Clifford-Hopf alternative k-deformed quantum Poincare algebra is investigated in the Atiyah-Bott-Shapiro mod 8 theorem context. The resulting algeb