1,368 research outputs found
Pseudoautomorphisms of Bruck loops and their generalizations
We show that in a weak commutative inverse property loop, such as a Bruck
loop, if is a right [left] pseudoautomorphism with companion , then
[] must lie in the left nucleus. In particular, for any such loop with
trivial left nucleus, every right pseudoautomorphism is an automorphism and if
the squaring map is a permutation, then every left pseudoautomorphism is an
automorphism as well. We also show that every pseudoautomorphism of a
commutative inverse property loop is an automorphism, generalizing a well-known
result of Bruck.Comment: to appear in Comment. Math. Univ. Caroli
Broken translation invariance in quasifree fermionic correlations out of equilibrium
Using the C* algebraic scattering approach to study quasifree fermionic
systems out of equilibrium in quantum statistical mechanics, we construct the
nonequilibrium steady state in the isotropic XY chain whose translation
invariance has been broken by a local magnetization and analyze the asymptotic
behavior of the expectation value for a class of spatial correlation
observables in this state. The effect of the breaking of translation invariance
is twofold. Mathematically, the finite rank perturbation not only regularizes
the scalar symbol of the invertible Toeplitz operator generating the leading
order exponential decay but also gives rise to an additional trace class Hankel
operator in the correlation determinant. Physically, in its decay rate, the
nonequilibrium steady state exhibits a left mover--right mover structure
affected by the scattering at the impurity.Comment: 30 pages, 4 figure
A characterization of the unitary and symplectic groups over finite fields of characteristic at least
The following characterization is obtained:
THEOREM. Let G be a finite group generated by a conjugacy class D of subgroups of prime order p ^ 5, such that for any choice of distinct A and B in D, the subgroup generated by A and B is isomorphic to Zp x Zp, L2(pm) or SL2(pm), where m depends on A and B. Assume G has no nontrivial solvable normal subgroup. Then G is isomorphic to Spn(q) or Un(q) for some power q of p
A 2-local characterization of M(12)
A characterization of the Mathieu group M(12) is established; the characterization is used by Aschbacher and Smith in their classification of the quasithin finite simple groups
The Status of the Classification of the Finite Simple Groups
The classification of the finite simple groups is one of the great theorems of recent mathematics. One of its principal participants reviews the result and current progress on understanding it
Finite groups acting on homology manifolds
In this paper we study homology manifolds T admitting the action of a finite group preserving the structure of a regular CW-complex on T. The CW-complex is parameterized by a poset and the topological properties of the manifold are translated into a combinatorial setting via the poset. We concentrate on n-manifolds which admit a fairly rigid group of automorphisms transitive on the n-cells of the complex. This allows us to make yet another translation from a combinatorial into a group theoretic setting. We close by using our machinery to construct representations on manifolds of the Monster, the largest sporadic group. Some of these manifolds are of dimension 24, and hence candidates for examples to Hirzebruch's Prize Question in [HBJ], but unfortunately closer inspection shows the A^-genus of these manifolds is 0 rather than 1, so none is a Hirzebruch manifold
From the microscopic to the van Hove regime in the XY chain out of equilibrium
Using the framework of rigorous algebraic quantum statistical mechanics, we
construct the unique nonequilibrium steady state in the isotropic XY chain in
which a sample of arbitrary finite size is coupled by a bond coupling
perturbation of arbitrary strength to two infinitely extended thermal
reservoirs, and we prove that this state is thermodynamically nontrivial.
Moreover, extracting the leading second order contribution to its microscopic
entropy production and deriving its entropy production in the van Hove weak
coupling regime, we prove that, in the mathematically and physically important
XY chain, the van Hove regime reproduces the leading order contribution to the
microscopic regime.Comment: 44 pages, 2 figure
A remark on the subleading order in the asymptotics of the nonequilibrium emptiness formation probability
We study the asymptotic behavior of the emptiness formation probability for
large spin strings in a translation invariant quasifree nonequilibrium steady
state of the isotropic XY chain. Besides the overall exponential decay, we
prove that, out of equilibrium, the exponent of the subleading power law
contribution to the asymptotics is nonvanishing and strictly positive due to
the singularities in the density of the steady state.Comment: 20 pages, 2 figure
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