The group K1(Sn) of the algebra of one-sided inverses of a polynomial algebra
نویسنده
چکیده
The algebra Sn of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting, left (but not two-sided) inverses of the canonical generators of the algebra Pn. The algebra Sn is a noncommutative, non-Noetherian algebra of classical Krull dimension 2n and of global dimension n and is not a domain. If the ground field K has characteristic zero then the algebra Sn is canonically isomorphic to the algebra K〈 ∂ ∂x1 , . . . , ∂ ∂xn , ∫
منابع مشابه
The group of automorphisms of the algebra of one-sided inverses of a polynomial algebra, II
The algebra Sn of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting, left (but not two-sided) inverses of the canonical generators of the algebra Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of auto...
متن کاملThe group of automorphisms of the algebra of one-sided inverses of a polynomial algebra
The algebra Sn in the title is obtained from a polynomial algebra Pn in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the Weyl algebra An and the polynomial algebra P2n. The group of automorphisms Gn of the algebra Sn is found: Gn = Sn ⋉ T n ⋉ Inn(Sn) ⊇ S...
متن کاملThe algebra of one-sided inverses of polynomial algebra
We study in detail the algebra Sn in the title which is an algebra obtained from a polynomial algebra Pn in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of Pn. The algebra Sn is non-commutative and neither left nor right Noetherian but the set of its ideals satisfies the a.c.c., and the ideals commute. It is proved that the classical Krull dimen...
متن کاملK1(S1) and the group of automorphisms of the algebra S2 of one-sided inverses of a polynomial algebra in two variables
Explicit generators are found for the group G2 of automorphisms of the algebra S2 of one-sided inverses of a polynomial algebra in two variables over a field of characteristic zero. Moreover, it is proved that G2 ≃ S2 ⋉ T 2 ⋉ Z ⋉ ((K∗ ⋉ E∞(S1))⊠GL∞(K) (K ∗ ⋉ E∞(S1))) where S2 is the symmetric group, T is the 2-dimensional torus, E∞(S1) is the subgroup of GL∞(S1) generated by the elementary matr...
متن کاملMax-Plus algebra on tensors and its properties
In this paper we generalize the max plus algebra system of real matrices to the class of real tensors and derive its fundamental properties. Also we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverses of tensors is characterized.
متن کامل