Utilitas matheseos. Jesuit Mathematics in the Clementinum between 1602 and 1773 (Prague, National Library of the Czech Republic - Mirror Chapel, 2nd November - 1st December 2002).
Let F be a finite field of characteristic p and K a field which contains a primitive pth root of unity and char K ≠ p. Suppose that a classical group G acts on the F-vector space V. Then it can induce the actions on the vector space \left [ V\bigoplus V \right ] and on the group algebra K\left [ V\bigoplus V \right ], respectively. In this paper we determine the structure of G-invariant ideals of the group algebra K\left [ V\bigoplus V \right ], and establish the relationship between the invariant ideals of K[V] and the vector invariant ideals of K\left [ V\bigoplus V \right ], and establish the relationship between the invariant ideals of K[V] and the vector invariant ideals of K\left [ V\bigoplus V \right ], if G is a unitary group or orthogonal group. Combining the results obtained by Nan and Zeng (2013), we solve the problem of vector invariant ideals for all classical groups over finite fields., Lingli Zeng, Jizhu Nan., and Obsahuje seznam literatury