coalgebra 中文意思是什麼
coalgebra
解釋
上代數-
We can give different structures on a tensor product h q to make it a bialgebra or hopf algebra. in [ 1 ] radford constructed a hopf algebra a x h with the smash algebra structure and the smash coproduct coalgebra structure, and pointed out that if a bialgebra b has a hopf subalgebra h and a projection ! : b - - > h, then there must be a subalgebra a of b such that b @ a x h is a bialgebra isomorphism
在張量積hq上可以給出不同的構造，使它成為雙代數或hopf代數， radford在文獻[ 1 ]中構造了以smash積為代數結構，余smash積為余代數結構的hopf代數a h ，並指出若b是雙代數， h是b的子hopf代數，且存在投射： b h （即是雙代數同態，且| _ h = id _ h ） ，則一定存在b的子代數a ，使ba h是雙代數同構。 -
Then we have : theorem 1 provided that h = be a weak hopf - coalgebra ; then we have : in the third section, we mainly study the - comudules : the weak hopf - comodules ; and we get the main results as : theorem 2 suppose c is a - coalgebra, then we say : ( a ) there is a one - to - one correspondence between ( isomorphic classses of ) right - comoduleover c and ( isomorphic classes of ) rational - graded left c * - modules
為c在訂上的模作用，它在直和項上的模作用形式為：上面三步影射依次為： z嗆p （叩廣。 ，山二clmhxclmhx ；吮z ；麗，遲兒的；是指q與c之間的自然匹配定理2設c為7t一余代數，則以下結論成立： （ a ） c上的右。 -
Lemma 7 h = be a weak hopf - coalgebra and is a normalized left integral of h1 ; then for all theorem 5 let h = be a finite - dimension weak hopf - coalgebra, then h is semisimple if and only if h1 is semisimple
一余代數，則下列命題等價： （ hi半單問hi中存在正規左積分iehi問hi是可分的卜代數引理5對弱hopf7t一余代數h khalh ，八，乙）而言1是從的正規積分有： voe 。 -
In section 5, we change the conditions of important theorems which are in section 3 and 4. we prove that the fundamental structure theorem still hold if a is a hopf algebra, and b a cleft comodule algebra or if a is a hopf algebra, and c a cocleft module coalgebra
第5節主要將第3 ， 4節主要定理的條件改變，分別討論當a是hopf代數， b是cleft余模代數時；和a是hopf代數， c是cleft模余代數時，基本結構定理仍然成立。 -
Lemma 5 let ( m, p ) be a right weak hopf - comoduleover h = a weak hopf - coalgebra, then for all ( 1 ) is a right submodule over ha of m. theorem 3 if h is a weak hopf - coalgebra and m = { ma } a is a right weak hopf - comodule over h ; we claim that : in the fourth section, we mainly study the weak integrals of h and the semisimplicity of h. we discuss the relation between the - integral and the antipiode of h, we get the following main results : lemma 6 let h = be a weak hopf - coalgebra, then the following statements for an element are equivalent ( a ) 1 a integral of h1 ( b ) ( c ) ( d ) ( e ) ( f ) is a right integral of h theorem 4 let h = be a weak hopf - coalgebra. then the following conditions on h1 are equivalent ( a ) h1 is semisimple
） ?喇） （ 1 ， 1 ） ）二m仰n m 」 」 「是m的右從子模定理3設h為弱hopf7t一余代數， m ma人h是h上的右弱hopf7t一余模n h是h在m上的余不動盧、 。則第四節我們主要討論了弱horf 。一余代數的半單性與h ；中的弱積分的關系；牙用（ h ，上門， l ） ， 3 ， si ）為弱hopf代數這一q點；我來觀察hi的正規弱積分與h的半單性之間的關系；該節第部分主要是給出弱hopf 。 -
Structural constants of finite dimension algebra and coalgebra
有限維代數及余代數的結構常數
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