Multiplicative invariant theory, as a research area in its own right within the wider spectrum
of invariant theory, is of relatively recent vintage. The present text offers a coherent account …

The classical Cayley map, $ X\mapsto (I_n-X)(I_n+ X)^{-1} $, is a birational isomorphism
between the special orthogonal group SO $ _n $ and its Lie algebra ${\mathfrak so} _n …

We give the complete stably rational classification of algebraic tori of dimensions $4 $ and
$5 $ over a field $ k $. In particular, the stably rational classification of norm one tori whose …

We consider the problem of whether the norm one torus defined by a finite separable field
extension K/k is stably (or retract) rational over k. This has already been solved for the case …

arXiv:1811.01676v4 [math.AG] 23 May 2019 Page 1 arXiv:1811.01676v4 [math.AG] 23 May
2019 RATIONALITY PROBLEM FOR NORM ONE TORI AKINARI HOSHI AND AIICHI …

Let Sn denote the symmetric group on n letters. We consider the Sn-lattice AnÀ1 fz 1,..., zn e
Znj i zi 0g, where Sn acts on Zn by permuting the coordinates, and its squares An2 nÀ1 …

We give a stably birational classification for algebraic tori of dimensions $3 $ and $4 $ over
a field $ k $. First, we define the weak stably equivalence of algebraic tori and show that …

Let $ k $ be a field and $ T $ be an algebraic $ k $-torus. In 1969, over a global field $ k $,
Voskresenskiǐ proved that there exists an exact sequence $0\to A (T)\to H^ 1 …

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k
and let 𝔤 be its Lie algebra. Let k (G), respectively, k (𝔤), be the field of k-rational functions …

We classify stably/retract rational norm one tori in dimension $ n-1$ for $ n= 2^ e $$(e\geq 1)
$ as a power of $2 $ and $ n= 12, 14, 15$. Retract non-rationality of norm one tori for …