Spinor norms of local autometries of generalized quadratic lattices

Yu. G. Teterin

Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 161-173

Résumé

It is proved that the group of spinor norms of autometries of a generalized quadratic lattice $\mathcal L$ over the ring of integral elements $v_\mathfrak p$ of a local field $k_\mathfrak p$, in the case where $\mathfrak p\nmid2$ and $\mathcal L$ is a generalized translation, is generated by the spinor norms of symmetries contained in the group of autometries of $\mathcal L$. As a corollary, an extension to the case of generalized quadratic lattices is given for known sufficient conditions of coincidence of the genus and the spinor genus of a quadratic lattice. Bibliography: 9 titles.