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The adjoint representation of fuzzy Lie algebras
Fuzzy Sets and Systems, 2001The author extends the notion of the commutator of a Lie algebra by Zadeh's extension principle to a product of fuzzy subsets. A fuzzy subspace generated by the product of two fuzzy ideals is shown to be a fuzzy ideal. The product of fuzzy ideals is used to define the descending central series of a fuzzy ideal.
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The Adjoint Representation of a Lie Group
1993Every group G acts on itself by inner automorphisms: the map associated with an element g is h ↦ ghg −1. If G is a Lie group, the differential of each inner automorphism determines a linear transformation on the tangent space to G at the identity element, because the identity is fixed by any inner automorphism.
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The “Adjoint” Equation and Representation of Solutions
1971In this section, we restrict our attention to the linear system $${\rm{\dot x}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{t}},{\rm{x}}_{\rm{t}} } \right)$$ (17.1) where L(t,ϕ) is continuous in t,ϕ, linear in ϕ and is given explicitly by $${\rm{L}}\left( {{\rm{t}},{\rm{\phi }}} \right) = \sum\limits_{{\rm{k}} = 1}^\infty {{\rm{A}}_{\rm{
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The adjoint representation of left distributive structures
Communications in Algebra, 1992We discuss some algebraic properties of the monoid generated by (left) translations in left distributive structures.This furnishes methods for enriching the original structure with a compatible associative product.
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Unitary Representations and Regularity for Self-adjoint Operators
1996In this chapter we specialize some of the considerations of Chap. 5 to the case of unitary C 0-groups in a Hilbert space ℋ. The theory of unitary representations W(x) = e iA·x of ℝ n is a very well understood classical subject and will not be presented here.
Werner O. Amrein +2 more
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Self-Adjoint Representations of Commutative *-Algebras
1990The results obtained in Section 8.4 have shown that a part of the representation theory of C*-algebras can be generalized to unbounded *-representations if, roughly speaking, the self-adjointness of certain *-representations is assumed. Thus seld-adjoint representations are basic objects in the theory of *-representations of general *-algebras. In this
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Representations of Non-Self-Adjoint Crossed Products [PDF]
Proceedings of the London Mathematical Society, 1983 Paul S. Muhly, Michael McAsey
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