Definitions
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 n. A closed subset of an algebra.
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Examples

Then a state is operationally separated with respect to T if T's application does not change the result of applying the state to any element of the other subalgebra: it is operationally separable with respect to T if it is operationally separated, either with respect to T, or with respect to some other operation T* that coincides with the action of T on the other subalgebra.

As I pointed out, the subalgebra generated by L_m with m 0 contains no reference to the conformal anomaly.

Hence this subalgebra admits a nilpotent BRST operator, and can be viewed as a gauge symmetry.

A subalgebra of an algebra is a set of elements of the algebra closed under the operations of the algebra.

N of natural numbers form a subalgebra of the powerset Boolean algebra 2N not isomorphic to the free Boolean algebra, but it has atoms, namely the singleton sets.

In fact, for every region R, you can find and define a subalgebra of the full algebra of operators, they argue.

h (A) is the subalgebra of B consisting of elements of the form h (a) for a in A.

(His proposal has been systematized by Gudder (1970), who takes a context C to be a maximal Boolean subalgebra of the lattice

For setfree formulations which, like those considered here, strictly adhere to a standard firstorder language with a denumerable supply of open formulas, the correct way of summarizing the algebraic strength of GEM is this: Any model of this theory is isomorphic to a Boolean subalgebra of a complete Boolean algebra with the zero element removed ” a subalgebra that is not necessarily complete if ZermeloFrankel set theory with the axiom of choice is consistent.

A von Neumann algebra is a *  subalgebra of the set of bounded operators B (H) on a Hilbert space H that is closed in the weak operator topology and contains the identity operator ” the
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