Small Deformations of Topological Algebras Mati Abel and Krzysztof Jarosz
... In this paper we extend the theory of small deformations to topological algebras. There are several ways to generalize the definition of a small deformation into the class of algebras equipped with a topology but without a norm. In the two sections following the Definitions and Notation we discuss two ...
... In this paper we extend the theory of small deformations to topological algebras. There are several ways to generalize the definition of a small deformation into the class of algebras equipped with a topology but without a norm. In the two sections following the Definitions and Notation we discuss two ...
INFINITESIMAL BIALGEBRAS, PRE
... Examples 2.2. Let (A, µ, ∆) be an ǫ-bialgebra. (1) A itself is an ǫ-Hopf module via µ and ∆, precisely by definition of ǫ-bialgebra. (2) More generally, for any space V , A⊗V is an ǫ-Hopf module via µ⊗id : A⊗A⊗V → A⊗V and ∆⊗id : A⊗V → A⊗A⊗V . (3) A more interesting example follows. Assume that the c ...
... Examples 2.2. Let (A, µ, ∆) be an ǫ-bialgebra. (1) A itself is an ǫ-Hopf module via µ and ∆, precisely by definition of ǫ-bialgebra. (2) More generally, for any space V , A⊗V is an ǫ-Hopf module via µ⊗id : A⊗A⊗V → A⊗V and ∆⊗id : A⊗V → A⊗A⊗V . (3) A more interesting example follows. Assume that the c ...
Algebras of Deductions in Category Theory∗ 1 Logical models from
... formulae is factored through the equivalence relation induced by equivalence of formulae, i.e. identity of truth-value for every valuation, one obtains the Lindenbaum algebra of classical propositional logic, which is a freely generated Boolean algebra, with as much free generators as there are prop ...
... formulae is factored through the equivalence relation induced by equivalence of formulae, i.e. identity of truth-value for every valuation, one obtains the Lindenbaum algebra of classical propositional logic, which is a freely generated Boolean algebra, with as much free generators as there are prop ...
Constructing Lie Algebras of First Order Differential Operators
... A realization of (g, k) in terms of first order differential operators is by definition a homomorphism ψ : g → D̂ + K[[x]] satisfying ψ(X) = φ(X) + c(X), X ∈ g for some realization φ of (g, k) in terms of derivations and some linear map c : g → K[[x]]. Given φ and c, the map ψ above is a homomorphis ...
... A realization of (g, k) in terms of first order differential operators is by definition a homomorphism ψ : g → D̂ + K[[x]] satisfying ψ(X) = φ(X) + c(X), X ∈ g for some realization φ of (g, k) in terms of derivations and some linear map c : g → K[[x]]. Given φ and c, the map ψ above is a homomorphis ...
Homomorphisms on normed algebras
... Theorem 2.3 cannot be applied since it is not known a priori that R is a Q-algebra in the norm \\T\\λ. If, however, the imbedding is discontinuous there exists a sequence {Tn} in R such that IITJIχ-^0 and ||5PJ|->oo. By the arguments of [1], the minimal ideals of R are the same as the minimal ideals ...
... Theorem 2.3 cannot be applied since it is not known a priori that R is a Q-algebra in the norm \\T\\λ. If, however, the imbedding is discontinuous there exists a sequence {Tn} in R such that IITJIχ-^0 and ||5PJ|->oo. By the arguments of [1], the minimal ideals of R are the same as the minimal ideals ...
2-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORIES
... same genus (i.e. number of holes). For a surface with boundary, we define the genus to be the number of holes of the surface after sewing in discs onto its boundary components. Thus, to classify connected cobordisms, we need to also specify the numbers of in-boundaries and the number out-boundaries ...
... same genus (i.e. number of holes). For a surface with boundary, we define the genus to be the number of holes of the surface after sewing in discs onto its boundary components. Thus, to classify connected cobordisms, we need to also specify the numbers of in-boundaries and the number out-boundaries ...
Weighted semigroup measure algebra as a WAP-algebra H.R. Ebrahimi Vishki, B. Khodsiani, A. Rejali
... W AP (A) = A∗ . Further information for the Arens regularity of Banach algebras can be found in [5, 6]. WAP-algebras, as a generalization of the Arens regular algebras, have been introduced and intensively studied in [9]. A Banach algebra A for which the natural embedding x 7→ x̂ of A into W AP (A)∗ ...
... W AP (A) = A∗ . Further information for the Arens regularity of Banach algebras can be found in [5, 6]. WAP-algebras, as a generalization of the Arens regular algebras, have been introduced and intensively studied in [9]. A Banach algebra A for which the natural embedding x 7→ x̂ of A into W AP (A)∗ ...
Separation of Variables and the Computation of Fourier
... over all arrows e such that the source of e is the target of P (equivalently, of Q), and ◦ denotes concatenation of paths. Thus, elements in these subalgebras are effectively determined by the initial “legs” of their paths. This is also equivalent to a choice of basis in the corresponding Wedderburn ...
... over all arrows e such that the source of e is the target of P (equivalently, of Q), and ◦ denotes concatenation of paths. Thus, elements in these subalgebras are effectively determined by the initial “legs” of their paths. This is also equivalent to a choice of basis in the corresponding Wedderburn ...
THE MIKHEEV IDENTITY IN RIGHT HOM
... This finishes the discussion of our results. The rest of this paper is organized as follows. In the next section, we recall some basic definitions regarding Hom-algebras and some properties of right Hom-alternative algebras. In section 3 we illustrate Corollary 1.2 by exhibiting an infinite family o ...
... This finishes the discussion of our results. The rest of this paper is organized as follows. In the next section, we recall some basic definitions regarding Hom-algebras and some properties of right Hom-alternative algebras. In section 3 we illustrate Corollary 1.2 by exhibiting an infinite family o ...