Maths Seminar of the School of Physical Sciences
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Simple Derivations on Tensor Product of Polynomial Algebras
Surjeet Kour
(Indian Institute of Technology, Gandhinagar)
Date: May 5, 2017 (Friday)
Time: 16:00 hrs (4:00 pm)
Venue: Seminar Room, First Floor, SPS, JNU
Abstract : Let A be a unique factorization domain containing a field k of characteristic zero and let A[X] and A[Y ] be two k-algebras. If d_1 and d_2 are k-derivations of A[X] and A[Y], respectively, then we have the unique k-derivation d_1 x 1 + 1 x d_2 of the tensor algebra A[X,Y] and it is usually denoted by d_1 \oplus d_2. If d_1 and d_2 are generalized triangular k-derivations of A[X] and A[Y], then the unique k-derivation d_1 \oplus d_2 of A[X,Y] is also a generalized triangular k-derivation. One can easily observe that if no ideal of A[X,Y] is (d_1 \oplus d_2)-invariant then neither d_1 nor d_2 has invariant ideals. In this talk we will discuss the converse of above statement for a large enough class of derivations.