分次赋值division algebras的酉SK1，I
Unitary SK1 of graded and valued division algebras, I
摘要：
具有酉对合的分次除代数的约化酉Whitehead群SK 1（即，第二类对合）且被无挠阿贝尔群分次.结果表明，在分级设置的计算是简单得多，比他们的nongraded同行。通过证明一个Hensel域上具有酉对合的驯服值除代数的酉SK 1与其相应的分次除代数的酉SK 1重合，建立了通向非分次情形的桥梁.因此，分级的方法使我们不仅可以恢复在文献中提供的结果与大大容易的证明，但也计算酉SK 1更广泛的类的分割代数在亨氏域。
英文摘要：
The reduced unitary Whitehead group SK1 of a graded division algebra equipped with a unitary involution (i.e., an involution of the second kind) and graded by a torsion-free abelian group is studied. It is shown that calculations in the graded setting are much simpler than their nongraded counterparts. The bridge to the non-graded case is established by proving that the unitary SK1 of a tame valued division algebra wih a unitary involution over a henselian field coincides with the unitary SK1 of its associated graded division algebra. As a consequence, the graded approach allows us not only to recover results available in the literature with substantially easier proofs, but also to calculate the unitary SK1 for much wider classes of division algebras over henselian fields.
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