Related papers: Four negations and the spectral presheaf
The fake monster Lie algebra is determined by the Borcherds function Phi_{12} which is the reflective modular form of the minimal possible weight with respect to O(II_{2,26}). We prove that the first non-zero Fourier-Jacobi coefficient of…
Nonassociative algebras satisfying the polynomial identities x(yz)=y(xz) and (xy)z=(xz)y are called bicommutative. We prove the following results: (i) Finitely generated bicommutative algebras are weakly noetherian, i.e., satisfy the…
In this paper we present analytic tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give…
In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson…
We study sympathetic Lie algebras, namely perfect and complete Lie algebras. They arise among other things in the study of adjoint Lie algebra cohomology. This is motivated by a conjecture of Pirashvili, which says that a non-trivial…
Braverman and Gaitsgory gave necessary and sufficient conditions for a nonhomogeneous quadratic algebra to satisfy the Poincare-Birkhoff-Witt property when its homogeneous version is Koszul. We widen their viewpoint and consider a quotient…
In a recent paper, Armoni, Shifman and Veneziano (ASV) gave a formal non-perturbative proof of planar equivalence between the bosonic sectors of SU(N) super Yang-Mills theory and of a gauge theory with a massless quark in the antisymmetric…
Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations on a category A in the category of categories over A are studied; in particular, the reflections and the coreflections of the latter in the…
Coalition Logic studies what coalitions can enforce. Recent work treats inability as simple non-ability: $\neg\Eff{C}\varphi$. This conflates two distinct configurations -- a coalition unable to force $\varphi$ may still force…
We use a Z_2-orbifold of the vertex operator algebra associated to the Niemeier lattice with root lattice A_3^8 and the no-ghost theorem of string theory to construct a generalized Kac-Moody algebra. Borcherds' theory of automorphic…
The First and Second Representation Theorem for sign-indefinite quadratic forms are extended. We include new cases of unbounded forms associated with operators that do not necessarily have a spectral gap around zero. The kernel of the…
Combining insights from the study of type refinement systems and of monoidal closed chiralities, we show how to reconstruct Lawvere's hyperdoctrine of presheaves using a full and faithful embedding into a monoidal closed bifibration living…
We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix…
Using Ohkawa's theorem that the collection of Bousfield classes is a set, we perform a number of constructions with Bousfield classes. In particular, we describe a greatest lower bound operator; we also note that a certain subset DL of the…
In this paper, we define and investigate a connexive logic, called 'Connexive semi-Heyting logic' (\mathcal{CSH} for short) and a new subvariety CSH of the variety SH of semi-Heyting algebras. It is shown that the logic \mathcal{CSH} is…
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
In the present paper we study the following problem: how to construct a coherent orthoalgebra which has only a finite number of elements, but at the same time does not admit a bivaluation (i.e. a morphism with a codomain being an…
A duality theorem of the bounded derived category of quasi-finite comodules over an artinian coalgebra is established. Let $A$ be a noetherian complete basic semiperfect algebra over an algebraically closed field, and $C$ be its dual…
Pseudo-effect algebras are partial algebraic structures, that were introduced as a non-commutative generalization of effect algebras. In the present paper, lattice ordered pseudo-effect algebras are considered as possible algebraic…
We give an elementary proof of the first fundamental theorem of the invariant theory for the orthosymplectic supergroup by generalising the method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic…