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