A (continuous) t-norm is called equationally definable when the corresponding standard BL-algebra [0, 1]∗ defined by ∗ and its residuum is the only (up to isomorphism) standard BL-algebra that generates the same variety Var([0, 1]∗). In this chapter we check that a continuous t-norm ∗ is equationally definable if and only if the t-norm is a finite ordinal sum of copies of the three basic contin...

Complexified spacetime algebra is defined as the geometric (Clifford) algebra of spacetime with complex coefficients. By resorting to matrix representation by means of Dirac-Pauli gamma matrices, the paper demonstrates isomorphism between subalgebras of CSTA and SU(3). It is shown that the symmetry group of those subalgebras is indeed U(1) ⊗ SU(2) ⊗ SU(3) and that there are 4 distinct copies of...

We study the basic monoidal properties of the category of Hopf modules for a coquasi Hopf algebra. In particular we discuss the so called fundamental theorem that establishes a monoidal equivalence between the category of comodules and the category of Hopf modules. We present a categorical proof of Radford’s S formula for the case of a finite dimensional coquasi Hopf algebra, by establishing a ...

Fix ρ : GQ,S → GL2(k) absolutely irreducible, and let ρ : GQ,S → GL2(R) be the universal deformation. We’re interested in the map R → Tm for some Hecke algebra defined in terms of ρ. Note that the Hecke algebra is 1-dimensional, and even finite free over Zp. The universal deformation ring R, however, often has dimension > 1 and nonzero p-torsion. In other words, the surjection R ։ Tm is not eve...

A number of combinations of theorem proving and computer algebra systems have been proposed; in this paper we describe another, namely a way to incorporate a logic in the computer algebra system Axiom. We examine the type system of Aldor { the Axiom Library Compiler { and show that with some modiications we can use the dependent types of the system to model a logic, under the Curry-Howard isomo...

We show that the weighted fusion category algebra of the principal 2-block b0 of GL2(q) is the quotient of the q-Schur algebra S2(q) by its socle, for q an odd prime power. As a consequence, we get a canonical bijection between the set of isomorphism classes of simple kGL2(q)b0-modules and the set of conjugacy classes of b0-weights in this case.

In this paper we define Baer BL-algebras as BL-algebras with the property that co-annihilator filters are generated by central elements. We use sheaf-theoretic techniques to construct a Baer extension of any BLalgebra, that is to embed any nontrivial BL-algebra A into a Baer BLalgebra A∗. The embedding turns to be an isomorphism if A is itself a Baer BL-algebra. 2000 MSC: 08A72, 03G25, 54B40, 0...

Nigel Higson and John Roe Abstract: We connect the assembly map in C∗-algebra K-theory to rigidity properties for relative eta invariants that have been investigated by Mathai, Keswani, Weinberger and others. We give a new and conceptual proof of Keswani’s theorem that whenever the C∗-algebra assembly map is an isomorphism, the relative eta invariants associated to the signature operator are ho...

Let A be a unital simple AT-algebra of real rank zero. Given an isomorphism γ1 : K1(A)→ K1(A), we show that there is an automorphism α : A → A such that α∗1 = γ1 which has the tracial Rokhlin property. Consequently, the crossed product A ⋊α Z is a simple unital AH-algebra with real rank zero. We also show that automorphism with Rokhlin property can be constructed from minimal homeomorphisms on ...