TY - BOOK ID - 65313414 TI - An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space PY - 2020 SN - 3030463664 3030463656 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Operator theory. KW - Mathematical physics. KW - Associative rings. KW - Rings (Algebra). KW - Topological groups. KW - Lie groups. KW - Operator Theory. KW - Mathematical Physics. KW - Associative Rings and Algebras. KW - Topological Groups, Lie Groups. KW - Groups, Lie KW - Lie algebras KW - Symmetric spaces KW - Topological groups KW - Groups, Topological KW - Continuous groups KW - Algebraic rings KW - Ring theory KW - Algebraic fields KW - Rings (Algebra) KW - Physical mathematics KW - Physics KW - Functional analysis KW - Mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:65313414 AB - This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference. ER -