Algebras Generated By Linearly Dependent Elements With Prescribed Spectra

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INDEX OF VOLUME 5

Herstein, I. N. A note on rings with central nilpotent elements, 620. Hochschild, G. Representations of restricted Lie algebras of characteristic p, 603. Honig, C. S. Proof of the well-ordering of cardinal numbers, 312, 1001. Horn, A. On the eigenvalues of a matrix with prescribed singular values, 4.

Our object is to investigate the deformations of LI (H(2n

Lk = Lk(H(2)) to be the Lie subalgebra of H(2) generated by the elements of degree greater than or equal to k. The two gradings on H(2) induce a bigraded structure on the cohomology groups. Let II2d w)(Li; L1) be the cohomology group of cocycles c such that deg(c(xl Ax2)) = d + d, + d2 if deg(x1) = di and wg(c(xl A X2)) = W + w1 + w2 if wg(xi

quasi-higher dimension - arXiv

from the ancestor model, depend also linearly (for the rational class), or trigonometrically on λ (for q-deformed class). For going beyond the prescribed form of the ancestor model, we search for a Lax matrix with higher scaling (or length) dimension linked to the integrable hierarchy and for introducing

DEFORMATIONS OF VECTOR FIELDS AND HAMILTONIAN VECTOR FIELDS

infinite-dimensional Lie algebras A is a new area of research. In the well-known work [1], A. Fialowski presents a complete description of the deformations of L (W( )), the nilpotent part of the Witt algebra. This and similar works like [2] and [3] show that the properties of deformations of nilpotent parts are com-

Construction and exact solution of a nonlinear quantum field

only linearly, while its q-deformation depends on its trigonometric functions [3,24]. Consequently, all quantum Lax matrices of known integrable models, since realized from the ancestor model, depend also linearly (for the rational class), or trigonometrically on λ (for q-deformed class). For going beyond the prescribed form of the