On initial algebras of multiplicative invariants

Abstract

Consider the ring of multiplicative invariants, k[A] G , of the group algebra k[A] of a faithful G-lattice A over base field k. Among other things, we will determine the cardinality of the set of all initial algebras, in (k[A] G ), of the ring of multiplicative invariants over all possible admissible orders on A.

A new class of finitely generated polynomial subalgebras without finite SAGBI bases

“…Moreover, #{in k[x] G | ∈ Ω 0 } is equal to |G| if G is generated by transpositions, and #R otherwise, where Ω 0 is the set of monomial orders on k[x] (cf. Kuroda's papers cited above, Tesemma [17] and Anderson et al [1]). This result is interesting because #{in [15]).…”

“…This result is interesting because #{in [15]). We mention that [6], [7], [11], [3], [17] and [1] treated more general classes of invariant rings than (1.1).…”