[A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [U] [V] [W] [X] [Y] [Z] [NOAUTHORS]
Xenos, Ph.J.

Classification of the homogeneous spaces of order six
Indian J. Pure Appl. Math. 18 (1987), N5, 385-401
Description: These homogeneous symmetric spaces (in terms of semisimple Lie algebras, their gradings, automorphisms, etc.) are classified.
Availability: 20005a54_385.pdf; journal's web site
Xie, Xiangdong

Tits alternative for closed real analytic 4-manifolds of nonpositive curvature
math.GR/0303131, 26 pages
Topology and its Applications Volume 136, Issues 1-3 , 28 January 2004, Pages 87-121
Abstract: We study subgroups of fundamental groups of real analytic closed 4-manifolds with nonpositive sectional curvature. In particular, we are interested in the following question: if a subgroup of the fundamental group is not virtually free abelian, does it contain a free group of rank two ? The technique involves the theory of general metric spaces of nonpositive curvature.
Xie, Luo Ping and Cao, You An

Automorphisms of the upper triangular matrix ring over commutative rings. (Chinese).
Natur. Sci. J. Xiangtan Univ. 24 (2002), no. 4, 1--5
Xin, Bin and Song, Guang'ai and Su, Yucai

Hamiltonian type Lie bialgebras
arXiv:math/0605669
Sci. China Ser. A 50 (2007), no. 9, 1267--1279
Description: For generalized Hamiltonian algebras, H^1(L, L\otimes L) = 0.
Xu, Ping

Noncommutative Poisson Algebras
DOI: 10.2307/2374983
American Journal of Mathematics, Vol. 116, No. 1 (Feb., 1994), pp. 101-125
Availability: 1994-noncommutative.pdf
Xu, Xiaoping

An analogue of the classical Yang-Baxter equation for general algebraic structures
DOI: 10.1007/BF01293592
Monatshefte für Math. 119 (1995), N4, 327-346
Description: CYBE for nonassociative algebras. Construction of some solutions for affine Lie algebras.
Availability: 1995-analogue.pdf

K-graded algebras and vertex operators
DOI: 10.1080/00927879508825222
Communications in Algebra, Volume 23, Issue 1 1995 , pages 291 - 311
Description: Some generaliztion of Virasoro in a Krichever-Novikov "almost graded" way and its central extensions.
Availability: 780042136.pdf

On simple Novikov algebras and their irreducible modules
DOI: 10.1006/jabr.1996.0356
Description: Classification in p>0. Closely related to Witt algebras.

Generalizations of the Block algebras
Manuscr. Math.
arXiv:math.QA/9911222, 31 pages
Abstract: Infinite-dimensional (super)algebras.

Poisson and Hamiltonian superpairs over polarized associative algebras
arXiv:math.QA/0010074, 30 pages
Abstract: Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic Poisson superpairs over a finite-dimensional or semi-finitely-filtered polarized $\Bbb{Z}_2$-graded associative algebra. Then we give a construction of certain Hamiltonian superpairs in the formal variational calculus over any finite-dimensional $\Bbb{Z}_2$-graded associative algebra with a supersymmetric nondegenerate associative bilinear form. Our constructions are based on the Adler mapping in a general sense. Our works in this paper can be viewed as noncommutative generalizations of the Adler-Gel'fand-Dikii Hamiltonian pair. As a preparatory work, some structural properties of polarized associative algebras have been studied.

Nongraded infinite-dimensional simple Lie algebras
arXiv:math.QA/0011264, 18 pages
Abstract: A survey.

Classification of simple Novikov algebras and their irreducible modules of characteristic 0
J. Algebra 246 (2001), no.2, 673-707
arXiv:math.QA/0008072

Construction of Gel'fand-Dorfman bialgebras from classical R-matrices
arXiv:math.QA/0208177, 10 pages
Description: Relationship between R-matrix and Novikov algebras. Lie algebras of the kind A \otimes C[t,t^{-1}] with bracket [a \otimes t^i, b \otimes t^j] = [a,b] \otimes t^{i+j} + iuv \otimes t^{i+j-1} - jvu \otimes t^{i+j-1} are mentioned.

Tree diagram Lie algebras of differential operators and evolution partial differential equations
J. Lie Theory 16 (2006), No. 4, 691--618
Abstract: A tree diagram is a tree with positive integral weight on each edge, which is a notion generalized from the Dynkin diagrams of finite-dimensional simple Lie algebras. We introduce two nilpotent Lie algebras and their extended solvable Lie algebras associated with each tree diagram. The solvable tree diagram Lie algebras turn out to be complete Lie algebras of maximal rank analogous to the Borel subalgebras of finite-dimensional simple Lie algebras. Their abelian ideals are completely determined. Using a high-order Campbell-Hausdorff formula and certain abelian ideals of the tree diagram Lie algebras, we solve the initial value problem of first-order evolution partial differential equations associated with nilpotent tree diagram Lie algebras and high-order evolution partial differential equations, including heat conduction type equations related to generalized Tricomi operators associated with trees.
Xue, Min and Lin, Weiqiang and Tan, Shaobin

Central Extension, Derivations and Automorphism Group for Lie Algebras Arising from the 2-Dimensional Torus
Journal of Lie Theory 16 (2006), No. 1, 139--153
Description: Virasoro-like algebra.
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