In this paper we determine the number of endomorphism rings superspecial abelian surfaces over a field $\mathbb{F}_q$ odd degree $\mathbb{F}_p$ in isogeny class corresponding to Weil $q$-number $\pm\sqrt{q}$. This extends earlier works T.-C. Yang and present authors on isomorphism classes these surfaces, also generalizes classical formula Deuring for supersingular elliptic curves. Our method is...

Via the introduction of (infinitary) disjunctions on any complete lattice while inheriting the meet as a conjunction, we construct a bijective correspondence (up to isomorphism) between complete lattices L and complete Heyting algebras DI(L) equipped with a so called disjunctive join dense closure operator RL. If L is itself a complete Heyting algebra then DI(L) ∼= L and RL = idDI(L). Ortholatt...

Most of the research in foundations of mathematics that I do in some way or another involves the use of nonstandard models. I will give a few examples, and indicate what is involved. 1. General algebra and measurable cardinals. An unexpectedly direct connection. 2. Borel selection and higher set theory. A descriptive set theoretic context extensively pursued by some functional analysts. 3. Equa...

The theory of the Clifford algebra of a vector space with a given symmetric bilinear form is rather well-understood: One of the basic properties of the Clifford algebra gives an explicit basis for it in terms of a basis of the underlying vector space (Theorem 1 below), and another one provides a canonical vector space isomorphism between the Clifford algebra and the exterior algebra of the same...

We construct a numeric algorithm for completing the proof of conjecture asserting that all deformed preprojective algebras generalized Dynkin type are periodic. In particular, we obtain an algorithmic procedure showing non-trivial types E7 and E8 exist only in characteristic 2. As consequence, show E6, periodic classification such algebras, up to algebra isomorphism. do it by reduction solution...

This paper is a contribution to the isomorphism problem for universal enveloping algebras of finite-dimensional Lie algebras. We focus on solvable small dimensions over fields arbitrary characteristic. prove, an field, that type metabelian algebra whose derived subalgebra has codimension one determined by its algebra. As application results in this paper, we solve dimension four characteristic ...

Wheeling: A Diagrammatic Analogue of the Duflo Isomorphism We construct and prove a diagrammatic version of the Duflo isomorphism between the invariant subalgebra of the symmetric algebra of a Lie algebra and the center of the universal enveloping algebra. This version implies the original for metrized Lie algebras (Lie algebras with an invariant non-degenerate bilinear form). As an application...

Let (R;G) be a pair consisting of an elliptic root system R with a marking G. Assume that the attached elliptic Dynkin diagram (R;G) is simply-laced (see Sect. 2). We associate three Lie algebras, explained in 1), 2) and 3) below, to the elliptic root system, and show that all three are isomorphic. The isomorphism class is called the elliptic algebra. 1) The rst one is the subalgebra e g(R) gen...

We introduce stabilised property $\Gamma$, a $\mathrm {C}^*$-algebraic variant of $\Gamma$ which is invariant under stable isomorphism. then show that simple separable nuclear {C}^*$-algebras with and {Cu}(A) \cong \mathrm {Cu}(A \otimes \mathcal {Z})$ absorb the Jiang-Su algebra $\mathcal {Z}$ tensorially.