# H * -algebra

## 0.1 H *-algebra

An H $*$-algebra is defined as a Hilbert space $\mathbb{A}_{H}$ equipped with an associative unital algebra structure and an antilinear involution ${}^{*}:\mathbb{A}_{H}\to\mathbb{A}_{H}$ which is compatible with taking the adjoint of the operators on the Hilbert space for the left and right multiplication of $\mathbb{A}_{H}$ with itself (ref. [1]).

## References

• 1 Baez, J. 2007. http://golem.ph.utexas.edu/category/2006/10/categorified_gelfandnaimark_th.htmlGroupoidification. (Preprint)
 Title H * -algebra Canonical name Halgebra Date of creation 2013-03-22 18:26:32 Last modified on 2013-03-22 18:26:32 Owner bci1 (20947) Last modified by bci1 (20947) Numerical id 7 Author bci1 (20947) Entry type Definition Classification msc 20G42 Classification msc 81R05 Classification msc 81R15 Classification msc 46N50 Related topic HilbertSpace Related topic QuantumSpaceTimes Related topic VonNeumannAlgebra Related topic WeakHopfCAlgebra2 Related topic CategoryOfHAlgebras