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The Z-grading determined by a long simple root of an affine or finite type Lie algebra arises from an adjoint or cominuscule representation of a lower rank semi-simple complex Lie algebra. Analysis of the relationship between the grading…

Representation Theory · Mathematics 2007-05-23 Meighan I. Dillon

In this paper we discuss metric theory associated with the affine (inhomogeneous) linear forms in the so called doubly metric settings within the classical and the mixed setups. We consider the system of affine forms given by $\qq\mapsto…

Number Theory · Mathematics 2020-06-03 Mumtaz Hussain , Simon Kristensen , David Simmons

Invariant affine reflection algebras are the last and the most general known extension of affine Kac-Moody Lie algebras, introduced in recent years. We develop a method known as "affinization" to the class of invariant affine reflection…

Quantum Algebra · Mathematics 2011-09-01 Saeid Azam , S. Reza Hosseini , Malihe Yousofzadeh

In this paper a construction of affine exterior algebra of Grassmann, with a special attention to the revisitation of this subject operated by Peano and his School, is examined from a historical viewpoint. Even if the exterior algebra over…

History and Overview · Mathematics 2010-02-23 Gabriele H. Greco , Enrico M. Pagani

We consider affine representable algebras, that is, finitely generated algebras over a field that can be embedded into some matrix algebra over a commutative algebra. We show that this algebra can in fact be chosen to be a polynomial…

Rings and Algebras · Mathematics 2021-07-23 Martin Lorenz

The Arithmetic is interpreted in all the groups of Richard Thompson and Graham Higman, as well as in other groups of piecewise affine permutations of an interval which generalize the groups of Thompson and Higman. In particular, the…

Group Theory · Mathematics 2009-09-14 Tuna Altınel , Alexey Muranov

In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…

Algebraic Geometry · Mathematics 2010-07-15 Feng-Wen An

Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…

Logic in Computer Science · Computer Science 2022-07-11 Luca Ciccone , Luca Padovani

We present an affine-intuitionistic system of types and effects which can be regarded as an extension of Barber-Plotkin Dual Intuitionistic Linear Logic to multi-threaded programs with effects. In the system, dynamically generated values…

Logic in Computer Science · Computer Science 2010-05-20 Roberto Amadio , Patrick Baillot , Antoine Madet

We present an affine-intuitionistic system of types and effects which can be regarded as an extension of Barber-Plotkin Dual Intuitionistic Linear Logic to multi-threaded programs with effects. In the system, dynamically generated values…

Logic in Computer Science · Computer Science 2009-12-03 Roberto Amadio , Patrick Baillot , Antoine Madet

We study the property of a normal scheme, that the complement of every hypersurface is an affine scheme. To this end we introduce the affine class group. It is a factor group of the divisor class group and measures the deviation from this…

Commutative Algebra · Mathematics 2009-09-29 Holger Brenner

Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…

Logic in Computer Science · Computer Science 2021-01-27 Vladimir Zamdzhiev

Classical primal-dual affine programming takes place over finite dimensional real vector spaces. This results in beautiful duality theory, connecting the optimal solu- tions of the primal maximization problem and the dual minimization…

Optimization and Control · Mathematics 2015-04-13 Tien Chih

Recently, Artemov [4] offered the notion of constructive consistency for Peano Arithmetic and generalized it to constructive truth and falsity in the spirit of Brouwer-Heyting-Kolmogorov semantics and its formalization, the Logic of Proofs.…

Logic in Computer Science · Computer Science 2019-05-28 Hirohiko Kushida

Since 2020, finite weight modules have been studied over twisted affine Lie superalgebras. To complete the characterization of modules over affine Lie superalgebras, we need some information regarding modules over untwisted affine Lie…

Representation Theory · Mathematics 2024-11-27 Asghar Daneshvar , Hajar Kiamehr , Maryam Yazdanifar , Malihe Yousofzadeh

We introduce and study several affine (=annular in this paper) versions of the classical diagram algebras such as Temperley-Lieb, partition, Brauer, Motzkin, rook Brauer, rook, planar partition, and planar rook algebras. We give generators…

Representation Theory · Mathematics 2025-12-22 David He , Daniel Tubbenhauer

This article considers some affine algebraic varieties attached to finite trees and closely related to cluster algebras. Their definition involves a canonical coloring of vertices of trees into three colors. These varieties are proved to be…

Quantum Algebra · Mathematics 2014-03-04 Frédéric Chapoton

General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables this, and how might…

Artificial Intelligence · Computer Science 2023-06-21 Gabriel Poesia , Noah D. Goodman

Peano Arithmetic is known to be provably equivalent to reflection over Elementary Arithmetic. We prove a characterization of Predicative Analysis in the guise of ATR0 in terms of stronger reflection principles.

Given a morphism from an affine semigroup Q to an arbitrary commutative monoid, it is shown that every fiber possesses an affine stratification: a partition into a finite disjoint union of translates of normal affine semigroups. The proof…

Combinatorics · Mathematics 2011-07-28 Ezra Miller