Search results for " Algebra"

Symplectic automorphisms of prime order on K3 surfaces

2006

The aim of this paper is to study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients. We determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the Coxeter-Todd lattice in the case of automorphism of order three. We also compute many explicit examples, with particular attention to elliptic fibrations.

From quantale algebroids to topological spaces: Fixed- and variable-basis approaches

2010

Using the category of quantale algebroids the paper considers a generalization of the classical Papert-Papert-Isbell adjunction between the categories of topological spaces and locales to partial algebraic structures. It also provides a single framework in which to treat the concepts of quasi, standard and stratified fuzzy topology.

Quantum extensions of semigroups generated by Bessel processes

1996

We construct a quantum extension of the Markov semigroup of the classical Bessel process of orderv≥1 to the noncommutative von Neumann algebra s(L2(0, +∞)) of bounded operators onL2(0, +∞).

Nilpotent Lie algebras with 2-dimensional commutator ideals

2011

Abstract We classify all (finitely dimensional) nilpotent Lie k -algebras h with 2-dimensional commutator ideals h ′ , extending a known result to the case where h ′ is non-central and k is an arbitrary field. It turns out that, while the structure of h depends on the field k if h ′ is central, it is independent of k if h ′ is non-central and is uniquely determined by the dimension of h . In the case where k is algebraically or real closed, we also list all nilpotent Lie k -algebras h with 2-dimensional central commutator ideals h ′ and dim k h ⩽ 11 .

Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets

2006

Let A be a uniform algebra, and let o be a self-map of the spectrum M A of A that induces a composition operator C o on A. The object of this paper is to relate the notion of "hyperbolic boundedness" introduced by the authors in 2004 to the essential spectrum of C o . It is shown that the essential spectral radius of C o , is strictly less than 1 if and only if the image of M A under some iterate o n of o is hyperbolically bounded. The set of composition operators is partitioned into "hyperbolic vicinities" that are clopen with respect to the essential operator norm. This partition is related to the analogous partition with respect to the uniform operator norm.

The parameterized local deduction theorem for quasivarieties of algebras and its application

1996

Let τ be an algebraic type. To each classK of τ-algebras a consequence relation ⊧ K defined on the set of τ-equations is assigned. Some weak forms of the deduction theorem for ⊧ K and their algebraic counterparts are investigated. The (relative) congruence extension property (CEP) and its variants are discussed.CEP is shown to be equivalent to a parameter-free form of the deduction theorem for the consequence ⊧ K .CEP has a strong impact on the structure ofK: for many quasivarietiesK,CEP implies thatK is actually a variety. This phenomenon is thoroughly discussed in Section 5. We also discuss first-order definability of relative principal congruences. This property is equivalent to the fact…

Group graded algebras and multiplicities bounded by a constant

2013

AbstractLet G be a finite group and A a G-graded algebra over a field of characteristic zero. When A is a PI-algebra, the graded codimensions of A are exponentially bounded and one can study the corresponding graded cocharacters via the representation theory of products of symmetric groups. Here we characterize in two different ways when the corresponding multiplicities are bounded by a constant.

Derivations on a Lie Ideal

1988

AbstractIn this paper we prove the following result: let R be a prime ring with no non-zero nil left ideals whose characteristic is different from 2 and let U be a non central Lie ideal of R.If d ≠ 0 is a derivation of R such that d(u) is invertible or nilpotent for all u ∈ U, then either R is a division ring or R is the 2 X 2 matrices over a division ring. Moreover in the last case if the division ring is non commutative, then d is an inner derivation of R.

An algebraic loop theorem and the decomposition of PD 3 -pairs

2006

On the regularity of the partial {$O\sp *$}-algebras generated by a closed symmetric operator

1992

Let be given a dense domain D in a Hilbert space and a closed symmetric operator T with domain containing D. Then the restriction of T to D generates (algebraically) two partial *-algebras of closable operators (called weak and strong), possibly nonabelian and nonassociative. We characterize them completely. In particular, we examine under what conditions they are regular, that is, consist of polynomials only, and standard. Simple differential operators provide concrete examples of all the pathologies allowed by the abstract theory.