crossed product meaning in Hindi

Examples

1. Skew polynomial rings are closely related to crossed product algebras.
2. There is also a construction in ring theory, the crossed product of rings.
3. An analogous theory has also been developed for actions on C * algebras and their crossed products.
4. A result by Doplicher, Haag and Roberts says that under some assumptions the crossed product can be recovered from the algebra of observables.
5. The Bunce Deddens algebras in fact are crossed products of the Cantor sets with a natural action by the integers "'Z " '.
6. Given a group action on a topological space, there is a corresponding crossed product which will in general be non-commutative even if the group is abelian.
7. This kind of ring ( see crossed product for a related construction ) can play the role of the " space of orbits " of the group action, in cases where that space cannot be approached by conventional topological techniques  for example in the work of Alain Connes ( cf . noncommutative geometry ).
8. The crossed product of a von Neumann algebra by a group " G " acting on it is similar except that we have to be more careful about topologies, and need to construct a Hilbert space acted on by the crossed product . ( Note that the von Neumann algebra crossed product is usually larger than the algebraic crossed product discussed above; in fact it is some sort of completion of the algebraic crossed product .)
9. The crossed product of a von Neumann algebra by a group " G " acting on it is similar except that we have to be more careful about topologies, and need to construct a Hilbert space acted on by the crossed product . ( Note that the von Neumann algebra crossed product is usually larger than the algebraic crossed product discussed above; in fact it is some sort of completion of the algebraic crossed product .)
10. The crossed product of a von Neumann algebra by a group " G " acting on it is similar except that we have to be more careful about topologies, and need to construct a Hilbert space acted on by the crossed product . ( Note that the von Neumann algebra crossed product is usually larger than the algebraic crossed product discussed above; in fact it is some sort of completion of the algebraic crossed product .)