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81.
82.
We compare the calculation of the two-loop -function in the N=1 supersymmetric electrodynamics regularized via higher derivatives and via dimensional reduction. We show that the renormalized effective action is the same for both regularizations. But in the method of higher derivatives, unlike in the dimensional reduction, the -function defined as the derivative of the renormalized coupling constant with respect to log turns out to be purely one-loop. The anomaly problem therefore does not occur in this regularization, because in the method of higher derivatives, the diagrams with counterterm insertions make a nonzero contribution, which is evaluated exactly in all orders of the perturbation theory. When dimensional reduction is used, this contribution is zero. We argue that this result is a consequence of the mathematical inconsistency of the dimensional reduction method and that just this inconsistency leads to the anomaly problem. 相似文献
83.
Abdullah?AltinEmail author Ay?egül?Eren?inEmail author 《Czechoslovak Mathematical Journal》2004,54(4):969-979
In this paper we obtain all solutions which depend only on r for a class of partial differential equations of higher order with singular coefficients. 相似文献
84.
The aim of this note is to give a short proof that 2-local derivations on , the matrix algebra over the complex numbers are derivations and to give a shorter proof that 2-local *-automorphisms on are *-automorphisms.
85.
L.?BoultonEmail author S.?A.?M.?Marcantognini M.?D.?Morán 《Letters in Mathematical Physics》2004,70(2):121-131
We consider a vector-valued Hermite-type basis for which the eigenvalue problem associated to the operator H
A,B
:=B(;
x
2
)+Ax
2 acting on
becomes a three-terms recurrence. Here A and B are 2 × 2 constant positive definite matrices. Our main result provides an explicit characterization of the eigenvectors of H
A,B
that lie in the span of the first four elements of this basis when AB BA.This revised version was published online in March 2005 with corrections to the cover date. 相似文献
86.
Under certain constraints on the characteristic of a field , the commutative standard enveloping q-algebra >B of a commutative triple system A over is defined. It is proved that(1) if the algebra B is simple, then the system A is simple;(2) if the system A is simple, then B either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals). 相似文献
87.
Varghese Mathai 《Geometriae Dedicata》2003,99(1):1-15
We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C*
r
(, )-bundle and connection, which can be used to construct a C*
r
(, )-index that lies in the Grothendieck group of C*
r
(, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem. 相似文献
88.
Structure of Degenerate Block Algebras 总被引:13,自引:0,他引:13
Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map
: A
A
F, we define a Lie algebra
=
(A,
) over F with basis {ex | x
A/{0}} and Lie product [ex,ey] =
(x,y)ex+y. We show that
is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der
of
is a complete Lie algebra. We describe the double extension D(
, T) of
by T, where T is spanned by the locally finite derivations of
, and determine the second cohomology group H2(D(
, T),F) using anti-derivations related to the form on D(
, T). Finally, we compute the second Leibniz cohomology groups HL2(
, F) and HL2(D(
, T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee. 相似文献
89.
A note on the spectrum of an upper triangular operator matrix 总被引:1,自引:0,他引:1
Mohamed Barraa Mohamed Boumazgour 《Proceedings of the American Mathematical Society》2003,131(10):3083-3088
Let be a upper triangular operator matrix acting on the Banach space . We investigate the set of the operators for which , where denotes the spectrum.
90.
Fangyan Lu 《Journal of Mathematical Analysis and Applications》2003,284(1):127-143
Let X be a real or complex Banach space. Let and be two nest algebras on X. Suppose that φ is an additive bijective mapping from onto such that φ(A2)=φ(A)2 for every . Then φ is either a ring isomorphism or a ring anti-isomorphism. Moreover, if X is a real space or an infinite dimensional complex space, then there exists a continuous (conjugate) linear bijective mapping T such that either φ(A)=TAT−1 for every or φ(A)=TA∗T−1 for every . 相似文献