任意域上的非标准导出等价
Non-standard derived equivalences over arbitrary fields
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中文总结 AI 辅助
该研究反驳了Hu等人关于Rickard导出等价问题的猜想，通过构造特征无关的非标准导出自等价，证明该问题在任意域上的答案均为否定。
中文摘要 AI 辅助
1991年，Rickard提出问题：同一域上有限维代数之间的每一个导出等价是否都是标准的。Hu、Xi和Zhang在二元域上构造了非标准导出等价，并猜想Rickard的问题在特征不等于2时答案为肯定。我们通过在每一个域上构造非标准导出自等价来反驳该猜想。事实上，每个域都存在无穷多个具有此类自等价的有限维代数。该证明是特征无关的，基于截断多项式代数上矩阵的超迹恒等式。我们还给出了有限域上的第二个族。因此，Rickard的问题在每一个域上的答案都是否定的。
英文摘要
In 1991 Rickard asked whether every derived equivalence between finite-dimensional algebras over a common field is standard. Hu, Xi and Zhang constructed non-standard derived equivalences over the field with two elements and conjectured that Rickard's question has a positive answer in characteristic different from two. We disprove this conjecture by constructing non-standard derived autoequivalences over every field. In fact, each field admits infinitely many finite-dimensional algebras with such autoequivalences. The proof is characteristic-free and is based on a supertrace identity for matrices over truncated polynomial algebras. We also give a second family over finite fields. Consequently, Rickard's question has a negative answer over every field.
