scholarly journals Algebraic analogue of the Atiyah completion theorem

2014 ◽  
Vol 16 (2) ◽  
pp. 289-306
Author(s):  
Alisa Knizel ◽  
Alexander Neshitov
Keyword(s):  
Completion Theorem

Completions of ordered magmas

1980 ◽  
Vol 3 (1) ◽  
pp. 105-116
Author(s):  
Bruno Courcelle ◽  
Jean-Claude Raoult
Keyword(s):  
Programming Languages ◽  
Semantics Of Programming Languages ◽  
Ordered Algebras ◽  
Completion Theorem

We give a completion theorem for ordered magmas (i.e. ordered algebras with monotone operations) in a general form. Particular instances of this theorem are already known, and new results follow. The semantics of programming languages is the motivation of such investigations.

scholarly journals A Bound on Permutation Codes

10.37236/2929 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Jürgen Bierbrauer ◽  
Klaus Metsch
Keyword(s):  
Projective Plane ◽  
Symmetric Group ◽  
Minimum Distance ◽  
Main Part ◽  
Latin Squares ◽  
Permutation Codes ◽  
Permutation Code ◽  
Mutually Orthogonal Latin Squares ◽  
Hamming Metric ◽  
Completion Theorem

Consider the symmetric group $S_n$ with the Hamming metric. A  permutation code on $n$ symbols is a subset $C\subseteq S_n.$ If $C$ has minimum distance $\geq n-1,$ then $\vert C\vert\leq n^2-n.$ Equality can be reached if and only if a projective plane of order $n$ exists. Call $C$ embeddable if it is contained in a permutation code of minimum distance $n-1$ and cardinality $n^2-n.$ Let $\delta =\delta (C)=n^2-n-\vert C\vert$ be the deficiency of the permutation code $C\subseteq S_n$ of minimum distance $\geq n-1.$We prove that $C$ is embeddable if either $\delta\leq 2$ or if $(\delta^2-1)(\delta +1)^2<27(n+2)/16.$ The main part of the proof is an adaptation of the method used to obtain the famous Bruck completion theorem for mutually orthogonal latin squares.

Completions of Boolean algebras of projections and weak-star closures of C*-algebras on dual Banach spaces

2011 ◽  
Vol 54 (2) ◽  
pp. 515-529
Author(s):  
Philip G. Spain
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Boolean Algebras ◽  
C Algebra ◽  
C Algebras ◽  
Weak Star ◽  
Weakly Closed ◽  
Operator Closure ◽  
Dual Banach Space ◽  
Completion Theorem

AbstractPalmer has shown that those hermitians in the weak-star operator closure of a commutative C*-algebra represented on a dual Banach space X that are known to commute with the initial C*-algebra form the real part of a weakly closed C*-algebra on X. Relying on a result of Murphy, it is shown in this paper that this last proviso may be dropped, and that the weak-star closure is even a W*-algebra.When the dual Banach space X is separable, one can prove a similar result for C*-equivalent algebras, via a ‘separable patch’ completion theorem for Boolean algebras of projections on such spaces.

Homology fibrations and the ?group-completion? theorem

1976 ◽  
Vol 31 (3) ◽  
pp. 279-284 ◽  
Author(s):  
D. McDuff ◽  
G. Segal
Keyword(s):  
Group Completion ◽  
Completion Theorem

Improvement of Bruck's completion theorem

1991 ◽  
Vol 1 (2) ◽  
pp. 99-116 ◽  
Author(s):  
Klaus Metsch
Keyword(s):  
Completion Theorem

Godeaux–Serre varieties and the étale index

2013 ◽  
Vol 11 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Benjamin Antieau ◽  
Ben Williams
Keyword(s):  
Representation Theory ◽  
Finite Groups ◽  
Function Fields ◽  
Projective Representation ◽  
High Dimensional ◽  
Index Problem ◽  
Completion Theorem

AbstractWe use Godeaux–Serre varieties of finite groups, projective representation theory, the twisted Atiyah–Segal completion theorem, and our previous work on the topological period-index problem to compute the étale index of Brauer classes α ∈ Brét(X) in some specific examples. In particular, these computations show that the étale index of α differs from the period of α in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Godeaux–Serre varieties in terms of projective representation theory.

scholarly journals A completion theorem for fusion systems

2020 ◽  
Vol 236 (2) ◽  
pp. 501-531
Author(s):  
Noé Bárcenas ◽  
José Cantarero
Keyword(s):  
Fusion Systems ◽  
Completion Theorem
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