We present the first 100 pc scale view of the dense molecular gas in the central ~ 1.3 kpc region of the type-1 Seyfert NGC 1097 traced by HCN (J=4-3) and HCO+ (J=4-3) lines afforded with ALMA band 7. This galaxy shows significant HCN enhancement with respect to HCO+ and CO in the low-J transitions, which seems to be a common characteristic in AGN environments. Using the ALMA data, we study the characteristics of the dense gas around this AGN and search for the mechanism of HCN enhancement. We find a high HCN (J=4-3) to HCO+ (J=4-3) line ratio in the nucleus. The upper limit of the brightness temperature ratio of HCN (v2=1^{1f}, J=4-3) to HCN (J=4-3) is 0.08, which indicates that IR pumping does not significantly affect the pure rotational population in this nucleus. We also find a higher HCN (J=4-3) to CS (J=7-6) line ratio in NGC 1097 than in starburst galaxies, which is more than 12.7 on the brightness temperature scale. Combined from similar observations from other galaxies, we tentatively suggest that this ratio appears to be higher in AGN-host galaxies than in pure starburst ones similar to the widely used HCN to HCO+ ratio. LTE and non-LTE modeling of the observed HCN and HCO+ lines using J=4-3 and 1-0 data from ALMA, and J=3-2 data from SMA, reveals a high HCN to HCO+ abundance ratio (5 < [HCN]/[HCO+] < 20: non-LTE analysis) in the nucleus, and that the high-J lines (J=4-3 and 3-2) are emitted from dense (10^{4.5} < n_H2 [/cc] < 10^6), hot (70 < Tkin [K] < 550) regions. Finally we propose that the high temperature chemistry is more plausible to explain the observed enhanced HCN emission in NGC 1097 than the pure gas phase PDR/XDR chemistry.