mutations and the derived picard group of the brauer star algebra abstract in this paper we show that the derived picard group trpic a of the brauer star algebra of type n t is generated by shift pic a and equivalences h i i 1 n in the case t 1 where h i were shown to satisfy the relations of the braid group on the affine diagram a n 1 by schaps and zakay illouz in the multiplicity free case we show that trpic a is generated by a slightly bigger set

on the restoration of translational invariance in the critical quantum ising model on a fibonacci chain the spectra of quasiperiodically modulated quantum ising chains are investigated for moderate values of the modulation strength a unified approach based on the lifting of the degeneracy between the left and right moving eigenmodes is proposed the local scaling behaviour reflecting partial restoration of translational invariance is established both the conformally invariant scaling for the lower modes and the multi fractal scaling for the higher ones are described in terms of the same quantity a simple but accurate calculational scheme is constructed where the rearrangement in the level spectra is due to the interaction between left and right moving modes of the periodic system as induced by the quasiperiodic modulation

on computing of arbitrary positive integer powers for one type of tridiagonal matrices of even order abstract this paper is an extension of the work on computing of arbitrary positive integer powers for one type of tridiagonal matrices applied mathematics and computation to appear in which the general expression of the l th power l n for one type of tridiagonal matrices of order n 2 p 1 p n is presented in this new paper we derive the general expression of the l th power l n for the same type of tridiagonal matrices of order n 2 p p n expressions of eigenvectors and jordan s form of the matrix and of transforming matrix and its inverse are given too

local critical behaviour at aperiodic surface extended perturbation in the ising quantum chain the surface critical behaviour of the semi infinite one dimensional quantum ising model in a transverse field is studied in the presence of an aperiodic surface extended modulation the perturbed couplings are distributed according to a generalized fredholm sequence leading to a marginal perturbation and varying surface exponents the surface magnetic exponents are calculated exactly whereas the expression of the surface energy density exponent is conjectured from a finite size scaling study the system displays surface order at the bulk critical point above a critical value of the modulation amplitude it may be considered as a discrete realization of the hilhorst van leeuwen model

critical behaviour in aperiodic systems the author considers layered systems with aperiodically modulated couplings and study the effect of inhomogeneity on the critical behaviour using scaling arguments a relevance irrelevance type criterion is formulated and for relevant inhomogeneities the scaling form of singular quantities is determined the author has performed exact calculations for the surface magnetization of aperiodic quantum ising chains and for a 1 1 dimensional directed polymer in a longitudinal aperiodic environment the results for both systems are in accord with scaling considerations for a marginal aperiodicity the critical exponents are found to be non universal

improved kinetic renormalisation group approach to diffusion limited aggregation an improved kinetic renormalisation group approach to diffusion limited aggregation is presented this approach is based on the growth process itself and accounts for the dispersity in the growth probabilities it yields the multifractal spectrum d q with better values at smaller q on the 2d square lattice the authors find df 1 694 for the fractal dimensions of the cluster and that of its interface and d 1 1 01 for the information dimension the former agrees with the simulation results df approximately 1 70 and the latter compares very well with the exact value d 1 1

on computing of arbitrary positive integer powers for one type of tridiagonal matrices in this paper we derive the general expression of the l th power email protected n for one type of tridiagonal matrices of order n 2p 1 email protected n

groups acting on affine algebras general actions of groups on commutative affine domains are studied we prove a finiteness theorem for orbits of ideals and an ergodic theorem inspired by results from the theories of group algebras and universal enveloping algebras this paper began as a reconsideration of ergodic theorems in the theory of group algebras 2 3 41 the philosophy of these results is the following if a is a lattice i e a group isomorphic to z7 and g is a group of automorphisms of a then g acts on the maximal spectrum of the group algebra k a thus g mixes up the points on a torus the ergodic theorems study the connections between the original action on a and the nature of orbits on the torus although one can obtain many analogues to classical theorems in ergodic theory in this way the program is ultimately insufficient one ought not confine the study to orbits of maximal ideals after all there are likely to be g invariant closed subsets of the torus which are not finite unions of closures of point orbits to account for these more complicated situations we introduce a simple minded but new notion to the theory of groups acting on rings it will turn out that this concept sheds light on old theorems concerning enveloping algebras of lie algebras and suggests new problems in commutative algebra for the remainder of the paper k denotes a commutative field and r is a commutative affine k algebra assume g is a group of k automorphisms of r we are particularly interested in the case that g is infinite the role played by maximal ideals above is taken over by g variant prime ideals a prime ideal p of r is g variant provided that p is maximal among all ideals q such that

ising model on an icosahedral quasilattice the ising model on the three dimensional icosahedral quasilattice is studied by use of a monte carlo simulation the authors treat both cases where the spins are located on the vertices of the lattice and the centres of the lattice they investigate the critical phenomena on the basis of finite size scaling it is shown that the critical exponents are universal among regular lattices and quasilattices the critical temperatures of both models are found to be higher than that of the simple cubic lattice though the average coordination numbers of the three lattices are all six

integral ring homomorphisms abstract the purpose of this paper is to extend the classical notion of integral extensions of commutative rings to homomorphisms of affine pi rings it generalizes previous work r pare and w schelter j algebra 53 1978 477 479 w schelter j algebra 40 1976 245 254 errata 44 1979 576 which assumed the existence of centralizing elements without such elements the close relation between integrality and module finiteness breaks down cf examples 1 3 1 4 but the geometric implications of integrality remain our main result theorem 6 3 is an analogue of chevalley s theorem that a homomorphism r s is integral if and only if the induced map on spectra is proper it is proved in sections 6 8 by combining a geometric analysis with some explicit estimates of degrees a corollary is that the composition of integral homomorphisms is integral proposition 6 10 the main new tools we use are central homomorphisms of a ring r to orders over dedekind domains which we call curves we prove theorem 5 13 that the boundary of any constructible set in x spec r contains a dense set of points accessible along such a curve this fact contains a description corollary 5 14 of the zariski topology on x as well as the theorem of bergman and small on degrees of representations corollary 5 15 some of the results of this paper were announced in m artin in proceedings international symposium on algebraic geometry kyoto 1977 pp 237 247

on computing of arbitrary positive integer powers for one type of even order symmetric anti pentadiagonal matrices in this paper we derive the general expression of the lth power l n for one type of symmetric anti pentadiagonal matrices of even order

exact sequences of inner automorphisms of tensors abstract we produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor our sequence generalizes known sequences for associative and non associative algebras in a manner similar to those our sequence facilitates inductive reasoning about and calculation of the groups of symmetries of a tensor the new insights these methods afford can be applied to problems ranging from understanding algebraic structures to distinguishing entangled states in particle physics

a scaling method for asymptotic analysis of power series a new method is proposed for asymptotic analysis of power series in the method the author uses the relation that an n term power series of a singular quantity with critical exponent beta behaves asymptotically like n beta at the phase transition point the method is tested on known series with satisfactory results and used to analyse the power series of the two dimensional three state potts model of enting in good agreement with den nijs conjecture

phase transition in aperiodic quantum ising models phase transition in the aperiodic quantum ising models were studied in which the transverse magnetic fields are uniform and the couplings are arranged according to the aperiodic sequences that are generated by two types of two tile inflation rules with initial condition a p b q a a a m11 b m12 b b a m21 b m22 m12 m21 not equal 0 and a a a m11 b m12 b b b m21 a m22 m12 m22 not equal 0 when the inflation rules have the pisot vijayaraghavan pv property in number theory the generated aperiodic systems undergo phase transition at the critical points when the inflation rules do not have the pv property it is found that only by changing the initial conditions the inflation rules can produce aperiodic systems exhibiting phase transition as well as aperiodic systems which do not exhibit any phase transition

walks on the penrose lattice the authors performed extensive monte carlo simulations for different types of walks random walks ideal chains and self avoiding walks on the penrose quasilattice the critical exponent nu for each process is found to be the same as for periodic two dimensional lattices thus universality seems to hold also for the penrose tiling

on computing of arbitrary positive integer powers for one type of even order skew symmetric tridiagonal matrices with eigenvalues on imaginary axis ii this paper is an extension of the work on computing of arbitrary positive integer powers for one type of even order skew symmetric tridiagonal matrices with eigenvalues on imaginary axis i appl math comput in press in which the general expression of the lth power l n for one type of tridiagonal matrices of order n 2p p n is given in this new paper we present the complete derivation of this general expression expressions of eigenvectors of the matrix and of the transforming matrix and its inverse are given too

radial fredholm perturbation in the two dimensional ising model and gap exponent relation we consider concentric circular defects in the two dimensional ising model which are distributed according to a generalized fredholm sequence i e at exponentially increasing radii this type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation the critical exponent of the local magnetization is obtained through finite size scaling using a corner transfer matrix approach in the extreme anisotropic limit it varies continuously with the amplitude of the modulation and is closely related to the magnetic exponent of the radial hilhorst van leeuwen model through a conformal mapping of the system onto a strip the gap exponent relation is shown to remain valid for such an aperiodic defect

endomorphisms of right ideals of the weyl algebra let a a k be the first weyl algebra over an infinite field k let p be any noncyclic projective right ideal of a and set s end p we prove that as k algebras s f a in contrast there exists a noncyclic projective right ideal q of s such that s end q thus despite the fact that they are morita equivalent s and a have surprisingly different properties for example under the canonical maps autk a pick a pick s in contrast autk s has infinite index in pick s introduction given a comnmutative domain r the first weyl algebra a r is defined to be the associative r algebra thus r is central subring generated by elements x and y subject to the relation xy yx 1 when no ambiguity is possible we write a for a r let f be a field of characteristic zero then a a f is a simple ring and indeed may be thought of as one of the nicest and most important examples of simple noetherian rings the initial motivation for this paper was the following result of smith if p is the noncyclic right ideal p x2a xy 1 a of a then end p t a as f algebras 11 note that as char f 0 a is a simple hereditary ring and so end p is automatically morita equivalent to a even worse as pedp ada 17 the full matrix rings m2 a and m2 end p are isomorphic thus any proof of smith s result must be fairly subtle and may therefore provide useful invariants for a the first main aim of this paper is to generalize smith s result to an arbitrary projective right ideal of a while the proof of this is harder than that of smith s result it does provide a more informative proof in the sense that unlike smith we do not and cannot require an explicit description of end p for the rest of this introduction k will denote a field of arbitrary characteristic and all isomorphisms of rings will be k algebra isomorphisms theorem a let p be a projective right ideal of a a k then end p a if and only if p is a cyclic right ideal of a see theorem 3 1 this has some easy corollaries corollary b let p and q be projective right ideals of a a k then end p end q if and only if p to q for some t e d k the division ring of fractions of a and a e autk a the group of k automorphisms of a received by the editors february 13 1986 1980 mathematics subject classification 1985 revision primary 16a65 16a72 16a19 supported in part by an nsf grant 1987 american mathematical society 0002 9947 87 1 00 25 per page

positive integer powers of certain complex tridiagonal matrices in this paper we firstly present a general expression for the entries of the rth email protected n power of a certain n square complex tridiagonal matrix in terms of the chebyshev polynomials of the first kind secondly we obtain a complex factorization formula for generalized fibonacci pell numbers obeying also classical fibonacci and pell numbers

picard groups and infinite matrix rings we describe a connection between the picard group of a ring with local units t and the picard group of the unital overring end tt using this connection we show that the three groups pic r pic fm r and pic rfm r are isomorphic for any unital ring r furthermore eaclh ele ment of pic rfm r arises from an automorphism of rfm r which yields an isomorphsm between pic rfm r and out rfm r as one applica tion we extend a classical result of rosenberg and zelinsky by showing that the group outr rfm r is abelian for any commutative unital ring r

on invertible bimodules and automorphisms of noncommutative rings in this article we attempt to generalize the result that for a commu tative ring r the outer automorphism group of i automorphisms of m r is abelian of exponent n it is shown that a slightly weaker stable version of the result is still valid for affine semiprime noetherian pi rings we also show that the automorphism group of an affine commutative domain of positive di mension acts faithfully on the spectrum of the domain we investigate other questions involving bimodules and automorphisms and extend a result of smith on the first weyl algebra as a fixed ring let r be a ring with 1 in this article we are interested in comparing the automorphism group of mn r the ring of x matrices over r and the automorphism group of r in particular if r is commutative it is a classical result that the outer automorphism group of r automorphisms of mn r is an abelian group of exponent dividing this can be restated in terms of invertible bimodules the result is equivalent to the easy fact that any projective rank one module x with nx free over a commutative ring has order dividing in the picent group of r see rz and ko in the noncommutative case there is still a well known relationship between automorphisms and the picard

nonperiodic ising quantum chains and conformal invariance in a recent paper luck investigated the critical behavior of one dimensional ising quantum chains with coupling constants modulated according to general nonperiodic sequences in this note we take a closer look at the case where the sequences are obtained from two letter substituion rules and at the consequences of luck s results at criticality they imply that only for a certain class of substitution rules is the long distance behavior still described by thec 1 2 conformal field theory of a free majorana fermion as for the periodic ising quantum chain whereas the general case does not lead to a conformally invariant scaling limit

a multi temperature kinetic ising model and the eigenvalues of some perturbed jacobi matrices in this paper we analyze the eigenvalues of some perturbed jacobi matrices the results contain as particular cases the known spectra of several classes of tridiagonal matrices studied recently as a motivation we discuss a three and a four temperature kinetic ising model that can be analyzed using some perturbed jacobi matrices the analytical results can also be used for the associated reaction diffusion systems to solve for the particle density

percolation in two dimensional quasicrystals by monte carlo simulations the authors examine whether or not two dimensional quasi periodic lattices belong to the same universality class as periodic lattices and they study bond and site percolation in penrose tiling and its dual lattice by making use of monte carlo simulations for the sake of comparison they also investigate percolation in periodic systems such as a square kagome and dice lattice for all these lattices they evaluate several critical exponents such as alpha related to the total number of clusters beta related to the percolation strength gamma related to the mean cluster size nu related to the correlation length tau related to cluster sizes and the fractal dimension d their results indicate that universality holds in two dimensional lattices with or without periodicity where the coordination number could be either single valued or multi valued