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Related papers: Unifying order structures for Colombeau algebras

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We introduce the universal unitarily graded A-algebra for a commutative ring A and an arbitrary abelian extension U of the group of units of A, and use this concept to give simplified proofs of the main theorems of co-Galois theory in the…

Number Theory · Mathematics 2015-06-26 Holger Brenner , Almar Kaid , Uwe Storch

We introduce and develop a structure theory of a new class of noncommutative rings - Galois orders, that generalize classical orders in noncommutative rings. Galois orders realized as certain subrings of invariants in skew semigroup rings.…

Representation Theory · Mathematics 2008-09-16 Vyacheslav Futorny , Serge Ovsienko

Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of…

Rings and Algebras · Mathematics 2020-02-03 Kristen Boyle , Kailash C. Misra , Ernie Stitzinger

We show that the basic categorical concept of an S-algebra as derived from the theory of Segal's Gamma-sets provides a unifying description of several constructions attempting to model an algebraic geometry over the absolute point. It…

Algebraic Geometry · Mathematics 2015-12-15 Alain Connes , Caterina Consani

It is widely claimed that the natural axiom systems$\unicode{x2013}$including the large cardinal axioms$\unicode{x2013}$form a well-ordered hierarchy. Yet, as is well-known, it is possible to exhibit non-linearity and ill-foundedness by…

Logic · Mathematics 2023-12-21 Hanul Jeon , James Walsh

A Lie algebroid is a generalization of Lie algebra that provides a general framework to describe the symmetries of a manifold. In this paper, we introduce Lie algebroid index theory and study the Lie algebroid Dolbeault operator. We also…

Differential Geometry · Mathematics 2024-03-21 Tengzhou Hu

In this note we generalize the definition of partial permutations of Ivanov and Kerov and we build a universal algebra which projects onto the m-centraliser algebra defined by Creedon. We use it to present a new proof for the polynomiality…

Combinatorics · Mathematics 2023-10-12 Omar Tout

We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…

Logic in Computer Science · Computer Science 2024-03-12 David M. Cerna

We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bialgebra is completely determined by its…

Quantum Algebra · Mathematics 2008-12-16 Jean-Louis Loday

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.

Rings and Algebras · Mathematics 2020-05-12 Loic Foissy , Dominique Manchon , Yuanyuan Zhang

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. As an…

Logic · Mathematics 2007-05-23 Benno van den Berg , Federico De Marchi

We introduce a universally applicable method, based on the bond-algebraic theory of dualities, to search for generalized order parameters in disparate systems including non-Landau systems with topological order. A key notion that we advance…

Statistical Mechanics · Physics 2013-08-02 E. Cobanera , G. Ortiz , Z. Nussinov

We consider distributions on a closed compact manifold $M$ as maps on smoothing operators. Thus spaces of certain maps between $\Psi^{-\infty}(M)\to \mathcal{C}^{\infty}(M)$ are considered as generalized functions. For any collection of…

Analysis of PDEs · Mathematics 2009-06-09 Shantanu Dave

Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…

Logic in Computer Science · Computer Science 2013-01-07 Zhaohua Luo

We present a geometric approach to defining an algebra $\hat{\mathcal G}(M)$ (the Colombeau algebra) of generalized functions on a smooth manifold $M$ containing the space ${\mathcal D}'(M)$ of distributions on $M$. Based on differential…

Functional Analysis · Mathematics 2007-05-23 Michael Grosser , Michael Kunzinger , Roland Steinbauer , James Vickers

We present a new method of analysis of associative algebras. This method bears a certain resemblance to the famous analysis of commutative $C^*$-algebras in which an important role is played by multiplicative functionals over the algebra.…

Rings and Algebras · Mathematics 2007-05-23 Vladimir Dergachev

We show spherical completeness of the ring of Colombeau generalized real (or complex) numbers endowed with the sharp norm. As an application, we establish a Hahn Banach extension theorem for ultra pseudo normed modules (over the ring of…

General Mathematics · Mathematics 2008-02-13 Eberhard Mayerhofer

In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…

Algebraic Geometry · Mathematics 2008-08-20 E. Daniyarova , A. Myasnikov , V. Remeslennikov

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…

Algebraic Geometry · Mathematics 2007-05-23 Ralph M. Kaufmann

We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to…

Logic in Computer Science · Computer Science 2016-08-14 Alexander Kurz , Daniela Petrişan , Jiří Velebil
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