Zinbiel algebra - Zinbiel algebra - Wikipedia

Yilda matematika, a Zinbiel algebra yoki ikki tomonlama Leybnits algebrasi a modul ustidan komutativ uzuk bilan bilinear mahsulot aniqlovchi shaxsni qondirish:

${ displaystyle (a circ b) circ c = a circ (b circ c) + a circ (c circ b).}$

Zinbiel algebralari tomonidan kiritilgan Jan-Lui Loday  (1995 ). Bu nom Jan-Mishel Lemir tomonidan Leybnits algebrasiga "qarama-qarshi" deb taklif qilingan.^[1]

Nosimmetrik mahsulot

${ displaystyle a star b = a circ b + b circ a}$

assotsiativ hisoblanadi.

Zinbiyel algebra - bu Koszul dual tushunchasi a Leybnits algebra. Bepul Zinbiel algebrasi tugadi V bo'ladi tensor algebra mahsulot bilan

${ displaystyle (x_ {0} otimes cdots otimes x_ {p}) circ (x_ {p + 1} otimes cdots otimes x_ {p + q}) = x_ {0} sum _ { (p, q)} (x_ {1}, ldots, x_ {p + q}),}$

bu erda summa hamma narsadan ustundir ${ displaystyle (p, q)}$ aralashtiriladi.^[1]

Adabiyotlar

• Djumadil'daev, A.S .; Tulenbaev, K.M. (2005). "Zinbiel algebralarining nilpotentsiyasi". J. Din. Boshqarish tizimi. 11 (2): 195–213.
• Ginzburg, Viktor; Kapranov, Mixail (1994). "Operazlar uchun koszul ikkilik". Dyuk Matematik jurnali. 76: 203–273. arXiv:0709.1228. doi:10.1215 / s0012-7094-94-07608-4. JANOB  1301191.
• Loday, Jan-Lui (1995). "Leybnits kohomologiyasi va ikkitomonlama Leybnits algebralari uchun kubok mahsuloti" (PDF). Matematika. Skandal. 77 (2): 189–196.
• Loday, Jan-Lui (2001). Dialgebralar va tegishli operadalar. Matematikadan ma'ruza matnlari. 1763. Springer Verlag. 7-66 betlar.
• Zinbiel, Giyom V. (2012), "Algebralar turlari ensiklopediyasi 2010", Guo, Li; Bay, Chengmin; Loday, Jan-Lui (tahrir), Operadalar va universal algebra, Sof, amaliy matematik va nazariy fizika bo'yicha Nankai seriyasi, 9, 217–298 betlar, arXiv:1101.0267, Bibcode:2011arXiv1101.0267Z, ISBN  9789814365116