**Beiträge zur Algebra und Geometrie <BR> Contributions to Algebra and GeometryVol. 40, No. 2, pp. 399-415 (1999)
**

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Orthogonal Gelfand-Zetlin Algebras I

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Volodymyr Mazorchuk

Mechanics and Mathematics Department, Kyiv Taras Shevchenko University, 64, Volodymyrska st., 252033 Kyiv, Ukraine, e-mail: mazorchu@uni-alg.kiev.ua

**Abstract:** \font\msbm=msbm10 \def\C{{\msbm C}} We define a class of associative algebras which are similar to the enveloping algebra of $gl(n,\C)$. We construct a family of simple Verma and generalized Verma modules over such algebras. We also investigate the two simplest classes of such algebras in detail. For the first class we construct all finite-dimensional modules and investigate an $\cal O$-category and for the second, we classify all simple weight modules.

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