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SEMINARS |
Seminar of Laboratory of Theory of Functions "Modern Problems of Complex Analysis"
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Grassmann and Stiefel manifolds as affine varieties M. Golasin'ski University of Warmia and Mazury in Olsztyn, Poland |
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Abstract: Let Recall that the Grassmann manifold We aim to examine the structure of Grassmann and Stiefel manifolds via their presentations as algebraic sets. The main result is: Theorem. (1) The tangent bundle $T G_{n,r}(\mathbb K) = \{(A, B) \in G_{n,r}(\mathbb K) \times M_n(\mathbb K); \overline{B}t = B, AB + BA = B\}$. (2) There is an algebraic isomorphism $T G_{n,r}(\mathbb K) \approx \mathrm{Idem}_{r,n}(\mathbb K)$, where $\mathrm{Idem}_{r,n}(\mathbb K) = \{A \in M_n(\mathbb K); A^2 = A, \mathrm{rk}(A) = r\}$. (3) the The joint project with Professor F.R. Gomez, Malaga, Spain. |