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185:, Mathematical Surveys and Monographs, vol. 168, Providence, RI: American Mathematical Society,
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226:(1971), "The order of the antipode of finite-dimensional Hopf algebra",
190:
181:
Hazewinkel, Michiel; Gubareni, Nadiya; Kirichenko, V. V. (2010),
183:
Algebras, rings and modules. Lie algebras and Hopf algebras
8:
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163:: the order of the antipode is 2
1:
228:Proc. Natl. Acad. Sci. U.S.A.
68:ΞΆ for some positive integer
316:
72:. The Taft algebra is the
144:to 0. The antipode takes
249:10.1073/pnas.68.11.2631
108:. The coproduct takes
136:β1. The counit takes
44:of large even order.
240:1971PNAS...68.2631T
92:with the relations
78:associative algebra
32:) that is neither
234:(11): 2631β2633,
200:978-0-8218-5262-0
60:with a primitive
18:Taft Hopf algebra
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286:
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191:10.1090/surv/168
315:
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80:generated over
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24:introduced by
16:In algebra, a
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300:Hopf algebras
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224:Taft, Earl J.
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76:-dimensional
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66:root of unity
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52:Suppose that
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39:
38:cocommutative
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27:
26:Earl Taft
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48:Construction
22:Hopf algebra
17:
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40:and has an
34:commutative
284:0222.16012
217:1211.16023
175:References
171:> 1).
140:to 1 and
294:Category
276:16591950
42:antipode
258:0286868
236:Bibcode
209:2724822
28: (
282:
274:
267:389488
264:
256:
215:
207:
197:
58:field
56:is a
20:is a
272:PMID
195:ISBN
167:(if
156:to β
152:and
120:and
100:=0,
96:=1,
88:and
36:nor
30:1971
280:Zbl
262:PMC
244:doi
213:Zbl
187:doi
148:to
124:to
112:to
84:by
64:th
296::
278:,
270:,
260:,
254:MR
252:,
242:,
232:68
230:,
211:,
205:MR
203:,
193:,
132:+
106:cx
104:=ΞΆ
102:xc
62:n'
246::
238::
189::
169:n
165:n
161:x
158:c
154:x
150:c
146:c
142:x
138:c
134:x
130:x
128:β
126:c
122:x
118:c
116:β
114:c
110:c
98:x
94:c
90:x
86:c
82:k
74:n
70:n
54:k
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