Automorphism Research Papers - Academia.edu (original) (raw)

A connected Lie group admitting an expansive automorphism is known to be nilpotent but all nilpotent Lie groups do not admit expansive automorphisms. In this article, we find sufficient conditions for 2-step nilpotent Lie groups to admit... more

A connected Lie group admitting an expansive automorphism is known to be nilpotent but all nilpotent Lie groups do not admit expansive automorphisms. In this article, we find sufficient conditions for 2-step nilpotent Lie groups to admit expansive automorphisms.

For a finite group G, the group Outcent pG of outer central automorphisms of pG only depends on the Morita equivalence class of pG, which allows reduction to a basic order for its calculation. If the group ring is strongly related to a... more

For a finite group G, the group Outcent pG of outer central automorphisms of pG only depends on the Morita equivalence class of pG, which allows reduction to a basic order for its calculation. If the group ring is strongly related to a graduated order, it is often possible to give an explicit description of the basic order (see [14, 13]). In this paper, we show that Outcent B 1 for a block B of pG with cyclic defect group. We also prove that Outcent B 3 0 A6 1 for the principal block B 3 0 A6 of 3A6; this allows us to verify a conjecture of Zassenhaus for the perfect group of order 1080.

We consider homogeneous varieties of linear algebras over an associative-commutative ring K with 1, i.e., the varieties in which free algebras are graded. Let F be a free algebra of some variety A of linear algebras over K freely... more

We consider homogeneous varieties of linear algebras over an associative-commutative ring K with 1, i.e., the varieties in which free algebras are graded. Let F be a free algebra of some variety A of linear algebras over K freely generated by a finite set X, EndF be the semigroup of endomorphisms of F, and AutEndF be the group of automorphisms of the semigroup EndF. We investigate structure of the group AutEndF and its relation to the algebraical and categorical equivalence of algebras from A. We define a wide class of R1MF-domains containing, in particular, Bezout domains, unique factorization domains, and some other domains. We show that every automorphism of semigroup EndF, where F is a free finitely generated Lie algebra over an R1MF-domain, is semi-inner. This solves the Problem 5.1 left open in [21]. As a corollary, semi-innerity of all automorphism of the category of free Lie algebras over R1MF-domains is obtained. Relations between categorical and geometrical equivalence of ...

Ontology classification—the computation of subsumption hierarchies for classes and properties—is one of the most important tasks for OWL reasoners. Based on the algorithm by Shearer and Horrocks [9], we present a new classification... more

Ontology classification—the computation of subsumption hierarchies for classes and properties—is one of the most important tasks for OWL reasoners. Based on the algorithm by Shearer and Horrocks [9], we present a new classification procedure that addresses several open issues of the original algorithm, and that uses several novel optimisations in order to achieve superior performance. We also consider the classification of (object and data) properties. We show that algorithms commonly used to implement that task are incomplete ...

If G G is a group of automorphisms of a C ∗ {C^ \ast } -algebra A A with identity, then G G acts in a natural way as a transformation group on the state space S ( A ) S(A) of A A . Moreover, this action is uniformly almost periodic if and... more

If G G is a group of automorphisms of a C ∗ {C^ \ast } -algebra A A with identity, then G G acts in a natural way as a transformation group on the state space S ( A ) S(A) of A A . Moreover, this action is uniformly almost periodic if and only if G G has compact pointwise closure in the space of all maps of A A into A A . Consideration of the enveloping semigroup of ( S ( A ) , G ) (S(A),G) shows that, in this case, this pointwise closure G ¯ \bar G is a compact topological group consisting of automorphisms of A A . The Haar measure on G ¯ \bar G is used to define an analogue of the canonical center-valued trace on a finite von Neumann algebra. If A A possesses a sufficiently large group G 0 {G_0} of inner automorphisms such that ( S ( A ) , G 0 ) (S(A),{G_0}) is uniformly almost periodic, then A A is a central C ∗ {C^ \ast } -algebra. The notion of a uniquely ergodic system is applied to give necessary and sufficient conditions that an approximately finite dimensional C ∗ {C^ \ast ...

In this paper we construct a sequence of eigenfunctions of the "quantum Arnold's cat map" that, in the semiclassical limit, show a strong scarring phenomenon on the periodic orbits of the dynamics. More precisely, those... more

In this paper we construct a sequence of eigenfunctions of the "quantum Arnold's cat map" that, in the semiclassical limit, show a strong scarring phenomenon on the periodic orbits of the dynamics. More precisely, those states have a semiclassical limit measure that is the sum of 1/2 the normalized Lebesgue measure on the torus plus 1/2 the normalized Dirac measure concentrated on any a priori given periodic orbit of the dynamics. It is known (the Schnirelman theorem) that "most" sequences of eigenfunctions equidistribute on the torus. The sequences we construct therefore provide an example of an exception to this general rule. Our method of construction and proof exploits the existence of special values of h for which the quantum period of the map is relatively "short", and a sharp control on the evolution of coherent states up to this time scale. We also provide a pointwise description of these states in phase space, which uncovers their "hy...

Ontology classification—the computation of subsumption hierarchies for classes and properties—is one of the most important tasks for OWL reasoners. Based on the algorithm by Shearer and Horrocks [9], we present a new classification... more

Ontology classification—the computation of subsumption hierarchies for classes and properties—is one of the most important tasks for OWL reasoners. Based on the algorithm by Shearer and Horrocks [9], we present a new classification procedure that addresses several open issues of the original algorithm, and that uses several novel optimisations in order to achieve superior performance. We also consider the classification of (object and data) properties. We show that algorithms commonly used to implement that task are incomplete ...

Abstract. An automorphic loop (or A-loop) is a loop whose inner mappings are automorphisms. Every element of a commutative A-loop generates a group, and (xy) −1 = x −1 y −1 holds. Let Q be a finite commutative A-loop and p a prime. The... more

Abstract. An automorphic loop (or A-loop) is a loop whose inner mappings are automorphisms. Every element of a commutative A-loop generates a group, and (xy) −1 = x −1 y −1 holds. Let Q be a finite commutative A-loop and p a prime. The loop Q has order a power of p if and only if every element of Q has order a power of p. The loop Q decomposes as a direct product of a loop of odd order and a loop of order a power of 2. If Q is of odd order, it is solvable. If A is a subloop of Q then |A | divides |Q|. If p divides |Q | then Q contains an element of order p. For each set π of primes, Q has a Hall π-subloop. If there is a finite simple nonassociative commutative A-loop, it is of exponent 2. 1.

Ontology classification—the computation of subsumption hierarchies for classes and properties—is one of the most important tasks for OWL reasoners. Based on the algorithm by Shearer and Horrocks [9], we present a new classification... more

Ontology classification—the computation of subsumption hierarchies for classes and properties—is one of the most important tasks for OWL reasoners. Based on the algorithm by Shearer and Horrocks [9], we present a new classification procedure that addresses several open issues of the original algorithm, and that uses several novel optimisations in order to achieve superior performance. We also consider the classification of (object and data) properties. We show that algorithms commonly used to implement that task are incomplete ...