Search results for "isomorphism"
showing 10 items of 62 documents
Representation Theorems for Solvable Sesquilinear Forms
2017
New results are added to the paper [4] about q-closed and solvable sesquilinear forms. The structure of the Banach space $\mathcal{D}[||\cdot||_\Omega]$ defined on the domain $\mathcal{D}$ of a q-closed sesquilinear form $\Omega$ is unique up to isomorphism, and the adjoint of a sesquilinear form has the same property of q-closure or of solvability. The operator associated to a solvable sesquilinear form is the greatest which represents the form and it is self-adjoint if, and only if, the form is symmetric. We give more criteria of solvability for q-closed sesquilinear forms. Some of these criteria are related to the numerical range, and we analyse in particular the forms which are solvable…
On exotic affine 3-spheres
2014
Every A 1 \mathbb {A}^{1} -bundle over A ∗ 2 , \mathbb {A}_{\ast }^{2}, the complex affine plane punctured at the origin, is trivial in the differentiable category, but there are infinitely many distinct isomorphy classes of algebraic bundles. Isomorphy types of total spaces of such algebraic bundles are considered; in particular, the complex affine 3 3 -sphere S C 3 , \mathbb {S}_{\mathbb {C}}^{3}, given by z 1 2 + z 2 2 + z 3 2 + z 4 2 = 1 , z_{1}^{2}+z_{2}^{2}+z_{3}^{2}+z_{4}^{2}=1, admits such a structure with an additional homogeneity property. Total spaces of nontrivial homogeneous A 1 \mathbb {A}^{1} -bundles over A ∗ 2 \mathbb {A}_{\ast }^{2} are classified up to G m \mathbb {G}_{m}…
The Period Isomorphism
2017
The aim of this section is to define well-behaved isomorphisms between singular and de Rham cohomology of algebraic varieties.
On the blockwise modular isomorphism problem
2017
As a generalization of the modular isomorphism problem we study the behavior of defect groups under Morita equivalence of blocks of finite groups over algebraically closed fields of positive characteristic. We prove that the Morita equivalence class of a block B of defect at most 3 determines the defect groups of B up to isomorphism. In characteristic 0 we prove similar results for metacyclic defect groups and 2-blocks of defect 4. In the second part of the paper we investigate the situation for p-solvable groups G. Among other results we show that the group algebra of G itself determines if G has abelian Sylow p-subgroups.
An Algebraic Approach to Knowledge Representation
1999
This paper is an attempt to apply domain-theoretic ideas to a new area, viz. knowledge representation. We present an algebraic model of a belief system. The model consists of an information domain of special kind (belief algebra) and a binary relation on it (entailment). It is shown by examples that several natural belief algebras are, essentially, algebras of flat records. With an eye on this, we characterise those domains and belief algebras that are isomorphic to domains or algebras of records. For illustration, we suggest a system of axioms for revision in such a model and describe an explicit construction of what could be called a maxichoise revision.
Logarithmic bundles of deformed Weyl arrangements of type $A_2$
2016
We consider deformations of the Weyl arrangement of type $A_2$, which include the extended Shi and Catalan arrangements. These last ones are well-known to be free. We study their sheaves of logarithmic vector fields in all other cases, and show that they are Steiner bundles. Also, we determine explicitly their unstable lines. As a corollary, some counter-examples to the shift isomorphism problem are given.
Abstract and concrete tangent modules on Lipschitz differentiability spaces
2020
We construct an isometric embedding from Gigli's abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give two equivalent conditions which characterize when the embedding is an isomorphism. Together with arguments from a recent article by Bate--Kangasniemi--Orponen, this equivalence is used to show that the ${\rm Lip}-{\rm lip}$ -type condition ${\rm lip} f\le C|Df|$ implies the existence of a Lipschitz differentiable structure, and moreover self-improves to ${\rm lip} f =|Df|$. We also provide a direct proof of a result by Gigli and the second author that, for a space with a strongly rectifiable decomposition, Gigli'…
Specht property for some varieties of Jordan algebras of almost polynomial growth
2019
Abstract Let F be a field of characteristic zero. In [25] it was proved that U J 2 , the Jordan algebra of 2 × 2 upper triangular matrices, can be endowed up to isomorphism with either the trivial grading or three distinct non-trivial Z 2 -gradings or by a Z 2 × Z 2 -grading. In this paper we prove that the variety of Jordan algebras generated by U J 2 endowed with any G-grading has the Specht property, i.e., every T G -ideal containing the graded identities of U J 2 is finitely based. Moreover, we prove an analogue result about the ordinary identities of A 1 , a suitable infinitely generated metabelian Jordan algebra defined in [27] .
Artin groups of spherical type up to isomorphism
2003
AbstractWe prove that two Artin groups of spherical type are isomorphic if and only if their defining Coxeter graphs are the same.
Some Generalizations of a Simion Schmidt Bijection
2007
In 1985, Simion and Schmidt gave a constructive bijection φ from the set of all length (n-1) binary strings having no two consecutive 1s to the set of all length n permutations avoiding all patterns in {123,132,213}. In this paper, we generalize φ to an injective function from {0,1}n-1 to the set Sn of all length n permutations and derive from it four bijections φ : P →Q where P⊆{0,1}n-1 and Q ⊂ Sn. The domains are sets of restricted binary strings and the codomains are sets of pattern-avoiding permutations. As a particular case we retrieve the original Simion–Schmidt bijection. We also show that the bijections obtained are actually combinatorial isomorphisms, i.e. closeness-preserving bije…