June 8th, 2018

Десять лет назад

Почти десять лет назад, или точнее сказать, 19-20 июня 2008 года, на Архиве обнародовалась четвертая версия моего препринта по полубесконечной гомологической алгебре:


По сравнению с предыдущей (мартовской) версией, в ней появилось доказательство теоремы сравнения полубесконечных гомологий и когомологий тейтовских алгебр Ли и связанных с ними полуассоциативных полуалгебр. Оно содержалось в аппендиксе D к основному тексту, написанном совместно с Сережей Архиповым. Задачу построения теории полубесконечных (ко)гомологий ассоциативных алгебраических структур можно было считать, таким образом, решенной.

Но, пожалуй, более важную роль -- как в дальнейшем развитии предмета, так и в моей последующей судьбе -- сыграло скромное замечание, добавленное в этой версии к аппендиксу A. В этом замечании впервые было сформулировано определение контрамодуля над топологическим ассоциативным кольцом.

Изучение этого понятия, его свойств и приложений, постепенно стало в последующие десять лет моим основным занятием.


Levy was assigned to the USS Franklin in 1816. He was met there with prejudice and ostracism. Soon afterwards, while dancing in full uniform at the Patriot’s Ball in Philadelphia, a somewhat drunk Lieutenant William Potter bumped Levy on the dance floor. After a second and then a third forceful collision, Levy turned and slapped Potter across the face. Enraged, Potter cursed Levy as a Jew, to which Levy responded, “That I am a Jew, I neither deny nor regret”. The two were separated and Potter led away. The following morning, Levy received a formal challenge to a duel. Levy was not anxious to fight a man over a dance-floor incident and offered to shake hands and forget the whole thing. Potter refused and they agreed to a pistol duel in a meadow in New Jersey, as dueling had been outlawed in Pennsylvania. Asked by the judge if he had anything to say, Levy asked permission to utter a prayer in Hebrew, the Shema, and then said, “I also wish to state that, although I am a crack shot, I shall not fire at my opponent. I suggest it would be wiser if this ridiculous affair be abandoned”, to which Potter replied, “Coward!”. Levy gave Potter the first shot, which went wide. Levy then simply pointed his pistol in the air and fired. Potter reloaded a second round and fired, again wide of the mark. Levy reloaded and again fired into the air. A third and fourth shot missed Levy, each time returned with harmless shots into the air. Finally, a fifth shot nicked Levy’s ear. After Potter loaded for a sixth shot, Uriah took careful aim and fired into Potters chest, killing him instantly. The affair created quite a stir in Philadelphia and the press who praised Levy for his honor. He was acquitted during his subsequent court martial. Judged to not have been the provocateur nor the aggressor, his case was dismissed. He was also acquitted by a jury in the civil indictment brought against him.