6A-Algebra and its representations

The Virasoro algebra and its representations in physics

In this report for the course “Lie algebras and quantum groups” at KTH I discuss the origin of the Virasoro algebra, give the physical motivation for studying its unitary irreducible highest weight representations, and examine the necessary and sufficient conditions for such representations to exist.

Real Forms of the Oscillator Quantum Algebra and Its Representations

We consider the conditions under which the q-oscillator algebra becomes a Hopf *-algebra. In particular, we show that there are at least two real forms associated with the algebra. Furthermore, through the representations, it is shown that they are related to su q 1/2 (2)

Max-Plus algebra on tensors and its properties

In this paper we generalize the max plus algebra system of real matrices to the class of real tensors and derive its fundamental properties. Also we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverses of tensors is characterized.

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

The Algebra of Fibonacci Representations