*-orderings and *-valuations on algebras of finite Gelfand-Kirillov dimension.
The paper studies the real *-spectrum of a finitely generated algebra with involution over \(\mathbb{C}\) of finite Gelfand-Kirillov dimension. It is shown that for such an algebra the stability indices associated to the real *-spectrum are bounded by the Gelfand-Kirillov dimension, as in the commutative case. Birkhoff-Witt algebras of finite dimensional Lie algebras with involution are examples of such algebras. The real *-spectrum of a Birkhoff-Witt algebra is examined in detail in the 2-dimensional case. The paper is motivated by works on relationships between *-orderings, *-valuations and the reduced theory of Hermitian forms over a skewfield with involution. See also \textit{M. Marshall} [Commun. Algebra 28, No. 3, 1157-1173 (2000; Zbl 0955.16029)].
scientific article; zbMATH DE number 1901786
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