Displaying similar documents to “The group of commutativity preserving maps on strictly upper triangular matrices”

Multiplicative maps that are close to an automorphism on algebras of linear transformations

L. W. Marcoux, H. Radjavi, A. R. Sourour (2013)

Studia Mathematica

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Let be a complex, separable Hilbert space of finite or infinite dimension, and let ℬ() be the algebra of all bounded operators on . It is shown that if φ: ℬ() → ℬ() is a multiplicative map(not assumed linear) and if φ is sufficiently close to a linear automorphism of ℬ() in some uniform sense, then it is actually an automorphism; as such, there is an invertible operator S in ℬ() such that φ ( A ) = S - 1 A S for all A in ℬ(). When is finite-dimensional, similar results are obtained with the mere assumption...

Combinatorial mapping-torus, branched surfaces and free group automorphisms

François Gautero (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We give a characterization of the geometric automorphisms in a certain class of (not necessarily irreducible) free group automorphisms. When the automorphism is geometric, then it is induced by a pseudo-Anosov homeomorphism without interior singularities. An outer free group automorphism is given by a 1 -cocycle of a 2 -complex (a standard dynamical branched surface, see [7] and [9]) the fundamental group of which is the mapping-torus group of the automorphism. A combinatorial construction...

On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices

Jinsong Chen, Yi Jia Tan (2006)

Czechoslovak Mathematical Journal

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Let n be a positive integer, and C n ( r ) the set of all n × n r -circulant matrices over the Boolean algebra B = { 0 , 1 } , G n = ⋃ r = 0 n - 1 C n ( r ) . For any fixed r -circulant matrix C ( C ≠ 0 ) in G n , we define an operation “ * ” in G n as follows: A * B = A C B for any A , B in G n , where A C B is the usual product of Boolean matrices. Then ( G n , * ) is a semigroup. We denote this semigroup by G n ( C ) and call it the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix C . Let F be an idempotent element in G n ( C ) and M ( F ) the maximal subgroup...

The Strong Anick Conjecture is true

Vesselin Drensky, Jie-Tai Yu (2007)

Journal of the European Mathematical Society

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Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K 〈 x , y , z 〉 over a field K of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of K 〈 x , y , z 〉 . In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We...